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ANALYSIS OF ROAD TRAFFIC ACCIDENTS IN
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SAUDI ARABIA
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by
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Gamal R. Elkahlout
A Master's
Thesis
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Submitted
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in
partial fulfilment of the
award of Master of Philosophy of
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of,. I'Technology .
August 1988
11
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by Gamal R. Elkahlout, 1988
the
requirements for the
Loughborough University
....
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In the name of God, the
Beneficent, the Merciful
"~I
,
"
ACKNOWLEDGEMENTS
I
would
like
supervisor Mr. B.A.
to
express
my
sincere
Moore· for his guidance,
appreciation
to
encouragement,
my
and
valuable assistance at every stage during the preparation of the
thesis.
Thanks are also due to my external supervisor Dr. A. Bener
of King Saud University for his unfailing support and constructive
criticism all along.
I am particularly indebted to Dr.
A.M.
Abouammoh for his
unflagging help in creating the necessary conditions that enabled
me to press on with my research.
Indeed, without his constant
encouragement and direction, it is doubtful that I would have been
able to complete this work.
Grateful acknowledgements are also due to those too numerous
to name who have in their separate ways helped me all along.
ABSTRACT
Road traffic accidents are a major problem in both developed
and
developing countries.
Saudi Arabia can be
Traffic
problems
considered as
in
the
Kingdom
of
reasonably representative
of
these problems in oil-rich and rapidly developing countries.
This thesis concentrates basically on modelling road traffic
accident variables in the different regions of Saudi Arabia and
investigates
principal
the
relationships
variables
amongst
considered
are:
these
the
number
injuries, fatalities, and traffic intensity.
methods
used
series
analysis
autoregressive
in the analysis
using
both
moving average
through some packages,
are
of
models.
The
accidents,
The main statistical
regression analysis
stationary
such as,
variables.
and
and
time
nonstationary
Computer aided
analysis
the Statistical Analysis System
(SAS) at King Saud University, and the MINI TAB and
GLIM packages
at Loughborough University of Technology, has been used together
with specially written Fortran Programmes where necessary.
The
main objective
of
the
study
is
to
find
appropriate
models to fit the road traffic accident variables under consideration and to emphasize the proper choice of models or methods in
addressing different aspects of traffic accidents.
It is found that the most important variables affecting the
modelling of the accident data in Saudi Arabia are population size
and the number of registered vehicles.
It is noted that the number
of issued driving licences contribute significantly to the number of
injuries and fatalities in Saudi Arabia.
For the time series analysis,
regressive models
it is found
of order 1 or 2 and
that the auto-
seasonal autoregressive
model of order 1 or 2, can provide satisfactory fits to the number
of accidents,
injuries and fatalities in Saudi Arabia over all,
and to these variables for the Riyadh region in particular.
Based on this study some assessment is made of how much risk
is involved in motor vehicle accidents and some recommendations as
to how they can be reduced.
CONTENTS
CHAPTER I
INTRODUCTION
1.1
General Introduction
1 .2
Magni tude of the Problem
3
1.3
Elements and effects of any Road Traffic Accidents
6
1.4
Nature of the Problem
8
1.5
Object of the Study
11
LITERATURE REVIEW
13
2.1
Introduction
13
2.2
Accident Causation
16
2.3
accident Reporting
20
2.4
The Problem in Saudi Arabia
22
DATA REPRESENTATION
26
3.1
Introduction
26
3·2
Daily Data
Monthly Data
27
Yearly Data
29
Comments and Discussion
30
CHAPTER II
CHAPTER III
3·3
3·4
3.5
Tables and Graphs
28
39
APPLICATION OF REGRESSION ANALYSIS
77
4. 1
Introduction
77
4.2
The Regression model
79
4·3
Theoretical Consideration
80
CHAPTER IV
4·3·1
4·3·2
4.3.3
4.3·4
4.3.5
4·3.6
Least squares method
Analysis of variance table
F-test for significance of regression
The coefficient of determination "R 2 ..
Partial F-test
Partial correlation
80
82
84
85
86
87
4.4
Testing of the residuals
89
4·5
4.6
Regression analysis by maximum R2 _ Criterion
91
Regression analysis by backward elimination and
forward selection procedures
4.7
4.8
The use of dummy variables
4·9
Results and discussion
Fitting a poisson regression
Aitkin's adequate subset approach
Backward elimination and forward selection
Procedures
Poisson regression
The use of dummy variables
Tables and Graphs
93
96
99
103
104
111
113
113
115
l
CHAPTER V
APPLICATION OF TIME SERIES MODELLING
138
5·1
Introduction
138
5·2
Theoretical Consideration
139
ARIMA
5·3·2
5.3.3
CHAPTER VI
Model Building Procedures
Some ARIMA Models
139
143
for Selected Data
157
l~odeing
Modelling the Daily Accidents, Injuries
and Fatalities in Riyadh Area
Modelling the Monthly Accidents, Injuries
and Fatalities in Saudi Arabia
l~odeing
the 110nthly Accidents, Injuries
and Fatalities in Riyadh Region
157
165
171
Results and Discussion
177
Tables and Graphs
181
CONCLUSIONS
APPENDIX
REFERENCES
A
AND
RECOMMENDATIONS
262
267
269
1
CHAPTER I
INTRODUCTION
1.1
GENERAL INTRODUCTION
It
is generally acknowledged that means of transport are
considered to be one of the most important indicators to the level
of development of any
country of the world,
whether
it
be
a
developed, developing, or under developed country.
There must be a system to regulate and develop the extent of
use of· the vehicles on the road, so the countries and governments
make rules and regulations applying to
vehicles,
such
as:-
age
of
registration of vehicle at
regulations
to
control
the
the people owning these
driver,
driving
traffic department,
their
use.
In
spite
and
licence,
many
other
of. all
these
regulations, and as a natural result of increasing the number of
the
vehicles,
there must
be
traffic
accidents
and
these
will
differ in their severity and effect.
In the Kingdom of Saudi Arabia development has been taking
place very rapidly.
The oil industry has played a major role in
development, but serious problems, including road accidents, have
increased as a result of development.
It is essential to reduce
the number and severity of accidents resulting from road traffic
incidents, and techniques have to be discussed in the light of
research undertaken in the Kingdom and overseas.
implemented must be appropriate to the Kingdom.
Techniques to be
2
Saudi Arabia is considered as a developing country which
\fill expand, its area about 2,253,000 squared kilometers and a
population
of
9.9
millions,
and
it
contains
all
the
usual
transport means.
It
Middle
owns
East
the
with
biggest
24
internal
interna tional airports,
there is
Dammam).
the
air
railroad
and
fleet
airports,
countries
three
three major seaports.
(420 kilometers
The, most important means
Arabia is by road.
amongst
of
of
the
which
are
In addition
long between Riyadh and
of transportation in Saudi
There are about 30000 kilometers of paved
roads, and 51226 kilometers of agricultural roads have been built
to connect 7500 rural villages.
With the rapid expansion of road construction and increasing
number of vehicles in Saudi Arabia, road traffic accidents have
increased and become a major problem as in other parts of the
world.
For example in 1985, 3276 people were killed and
22630
people were injured as a result of 24594 road traffic accidents in
Saudi Arabia.
Over the past fifteen years many good roads have been built,
dual carriage ways, motorways and by-passes round towns.
Such
roads are necessary to reduce congestion and keep traffic moving.
Each year Saudi Arabia builds many roads but imports on average
300,000 cars per-year, so the congestion gets worse.
3
1.2
MAGNITUDE OF THE PROBLEM:
There are many factors which contribute in various ways to
the road traffic accidents problem in Saudi Arabia.
These factors
can be summarized in the following:
1.
SOCIO-ECONOMIC:
The high income of people in Saudi Arabia and the low taxes
on the vehicles, in addition to the low price of petrol.
It is
more economical and accessible to own a car than to rent one or to
use public transportation.
2.
POPULATION:
With the rapid economic development in Saudi Arabia,
has been a big increase in population.
there
The increasing of internal
immigration from rural area to- urban area to get a better social
life.
The traditional practice requires Saudi people to
carry
their families by special means rather than to rent a vehicle or
use public transport,
so the most sui table
transport means
for
this purpose is to own a private car.
3.
GEOGRAPHICAL:
Saudi Arabia is a big country and the cities,
villages are mostly far from each other.
towns has
been horizontal and
few
towns and
Expansion of cities and
high buildings
exist.
The
nature of the weather in Saudi Arabia is warm in most months of
the year, specially in the Riyadh region.
All these points increase the importance of using vehicles
as the best and most comfortable modern method, both for transport
of the people and for goods.
4
4.
NUMBER OF REGISTERED VEHICLES:
Vehicle ownership rates in Saudi Arabia are in general in-
creasing and rising fast.
As a result road traffic accidents are
fast
public
becoming
a
major
problem,
differences from accidents in the
with
some
distinct
industrialized nations.
The
number of registered vehicles in Saudi Arabia in 1982 was 3018811
which was more than ten times that of 1972, 180185 vehicles.
It
is not uncommon for ownership levels to increase ten times in a
ten year period.
5.
LAW ENFORCEMENT:
Traffic regulations in Saudi Arabia are not clear to some
drivers, specially unlicensed drivers where i t found that 32% of
the drivers involved in the road traffic accidents in Saudi Arabia
during the period of (1978-1985) are unlicenced drivers.
people tend to disobey traffic law and regulation,
and few,
any, penalties are given by the law enforcement agents.
19 driving schools issue
The
instruction
of
l~any
if
More than
the driving licenses in Saudi Arabia.
these
schools
are
theoretical
more
than
practical and the driving lessons are not in the field but within
the limits of the school, so this method gives little experience
to
the
drivers.
Periodical
inspection
of
the
vehicles
are
required by the traffic departments.
6.
ENTERTAINMENT:
Most adult drivers and their families
use
their cars for
passing the time in afternoon and evening, because of lack of outdoor entertainment facilities available and this incidentally is
the time when most of the 'accidents occur.
"
5
7.
RELIGIOUS:
Millions of muslims from all over the world visit the ho ly
places
in Saudi
Arabia
each year,
for
example
in
1985,
vehicles entered Saudi Arabia during the Haj season to
98433
the holy
places which are Makkah and Madinah, and as a result the number of
road traffic accidents naturally increased.
8.
DRIVING LICENCE:
There are a substantial number of drivers
who are not licensed.
enforcement
drivers.
and
to
in Saudi Arabia
This might be related to the lack of law
educational
and
cultural
differences
The number of driving licences issued has
31542 in 1971
to 340,333 in" 1985.
of
jumped from
There is a gap between
the
number of registered vehicles and the number of driving licences.
Some of the reasons for the gap are attributed to
rate
of
imported
vehicles,
the
very
poor
law
the increased
enforcement
concerning driving without a driving licence, and to the fact that
a number of people own more than one car.
In general,
the major problems in measuring magni tudes of
traffic accidents arise from the following:
i)
Accident reporting thresholds vary from place to place
and time to time.
11)
Accident reports are not always filled out completely.
iii)
Exposure data are not always readily available (some
exposure data can be obtained from traffic records).
iV)
Inaccurate data can misrepresent the magnitude of the
problem.
6
1.3
ELEMENTS AND EFFECTS OF ROAD TRAFFIC ACCIDENTS:The main reasons for any road traffic depends first on the
driver, secondly on the vehicle, and finally on the road.
traffic accidents studies report
that driver fault
Most
ratio
in an
accident is about 80%, the vehicle 15%, and the road 5%.
The elements of any road traffic accident are:-
THE DRIVER:
1.
The
fitness,
marital
important
tuition.
status,
aspects
The
of
effect
nationality,
the
of
driver
drugs,
and
are
alcohol
educational
age,
medical
and
fatigue,
level.
Driver
faults, in general, depend on several factor"s such as,
a)
Behavioural factor:
that is the good recognition of
(and speedy reaction against) the faults of others,
are
drivers,
pedestrians,
animals,
or
any
other
whether they
users
of
the
road.
b)
Physical factor:
That is the ability of the nervous
system of the driver to escape from others faults.
The driver
must be in a good psychological state prior to and while he is
driving the vehicle.
c)
Familari ty with traffic rules and regulations:
driver must know the nature,
The
rules, and theory of driving and be
familiar with the parts of the vehicle, to drive the car correctly
and to be less of a risk to others.
general
rules
accidents.
gives
the
driver
a
Because knowledge of the
better
chance
of
avoiding
7
II.
THE VEHICLE:
There are two factors to vehicle design, first factors that
help in preventing accidents such as:
Brakes, tyre tread depth,
indicators, and all round visibility, second factors that protect
the occupants when an accident does occur, such as the passenger
cell compartment, seat belts, head rests, etc.
The factors for safety and security of the occupants unfortunately are incomplete in most of the imported vehicles in
Saudi Arabia,
so the government
puts some
conditions on manu-
facturing imported vehicles to be more suitable to the weather and
conditions in Saudi Arabia and to increase safety.
IH.
THE ROAD:
The roads in Saudi Arabia can claim to be amongst the best
in the developing countries.
For example in Riyadh there are
about 92 kilometers of freeways around the city, and roads inside
the city are of the dual type and contain many concrete and metal
flyovers for vehicles and for pedistrians.
the
inter-sections
involve,
road
include
engineering,
traffic
road
signals.
safety,
In addition most of
The
road
education,
traffic law enforcement.
The effects of road traffic accidents are:-
factors
and
road
8
I.
ECONOMIC EFFECT:
This is
formidable because
of
the
large
number of
road
traffic accidents that lead to either death or total disability,
or to a prolonged absence from work as a
tion,
sick
leave,
and
the
need
fo~
t of hospi taliza~esul
further
sociomedical
rehabilitation.
11.
HUMAN EFFECT:
Nothing can compensate the loss of a productive human life.
They
reduce
the
capability
productive capacity.
of
the
nation
to
increase
its
An average of 2139 people dead each year in
the period of (1971-1985), and large numbers of human disabilities,
all of these losses are important in holding back the development
of the country.
Ill.
SOCIAL EFFECT:
The social problems that arise from road traffic accidents
are loss or disability of a member of the
family,
diminished
prospects leading to the total or partial reduction in earning
capacity, and effect of the social position of the handicapped and
his family with the resulting psychological stresses.
1.4
NATURE OF THE PROBLEM:
Road traffic accidents constitute one of the major problems
of modern daily life.
This is almost equally as acute in under-
developed or developing societies as in the industrialized ones.
9
Saudi Arabia is no exception.
Indeed, given the doubling of
vehicle ownership at short and regular intervals, as well as the
ready availability of petrol at a remarkably low price,
it was
perhaps to be expected that the number of traffic accidents would
rise
dramatically.
Nonetheless,
the
rate
at
which
such
an
increase has taken place has been far more than many would have
anticipated, and far exceeds that of other adjacent oil producing
countries.
Motor
vehicle
accidents
have
become
one
of
the
major
problems in Saudi Arabia, despite the prohibition against sale and
consumption of alcohol as mandated by Islamic Law and the ban of
women drivers that substantially reduce the number of vehicles on
the road.
Riyadh
is
population about
the
capital
city
of
Saudi
1.8 million in 1985 • It
challenging cities in terms
of
is
Arabia,
and
its
one
the
most
of
traffic problems and accidents.
The sUdden increase in its population and wealth has led to an
almost
commensurate
rise
in
automobile
ownership
on
an
unprecedented scale.
The growth in the number of traffic accidents has been so
serious that
aspect
it has not
only
proved debilitating to
of traffic management and control,
but
has
the whole
also
become
deleterious to the entire socio-economic fabric of the country.
Both the government and the public at large need to take active
measures in order to reduce the losses, both human and material.
Without. such concerted action, the size of these serious losses is
likely to increase, even double, within the next few years.
10
Al though the relationship between accident involvement and
various
socio-economic
factors
has
been
investigated
in
most
countries, this has not been done for the Kingdom of Saudi Arabia.
Furthermore, the results obtained for other countries may not be
applicable to the Kingdom of Saudi Arabia because of its somewhat
unique character and socio-economic evalution.
This facto rs can
be summarized as follows:1 -
The enormous growth in the number of registered vehicles,
which increased from 144768 in 1971
to 4144248 by
the end
of
1985.
2 -
The fast pace of motorization has not been paralleled by
development
in
driving
education,
law
enforcement,
and
other
safety related areas.
3 -
The presence of large numbers of expatriates from all over
the world where i t found that 42% of the drivers involved in the
road traffic accidents in Saudi Arabia during the period (19781985) are non-Saudi drivers.
These people come from different
cultures with different habits, attitudes and value systems.
Such
wide differences in background may create safety-related problems
on the roads.
4 -
With rapid economic development and fast industrialization
in the Kingdom of Saudi Arabia there has been an enormous increase
in the intensity of traffic-flow.
5 -
The apparent disposition and affinity towards high speed
among the drivers is the major cause of accidents.
of the accidents
About 60-65%
in Saudi Arabia have been attributed
speed.
.,
to high
11
1.5
OBJECT OF THE STUDY:
The objective of the study is to identify and develop the
components of motor vehicle accidents information system in the
Kingdom of Saudi Arabia,
necessary
epidemiological
which would provide
and
statistical
the essential and
base
for
Planning,
Programming, Managing and Evaluating measures aiming at reducing
severity and frequency of road traffic accidents.
This project has the following objectives:-
1)
To introduce a literature review of road traffic accidents
and their severity in the world in general,
and in Saudi
Arabia
road
in
particular.
Factors
affecting
traffic
accidents will be described.
2)
The available data to be used in the present study will be
discussed with tlie help of some graphical representation.
Some basic statistics relating to accidents,
injuries
and
fatali ty rates will be calculated.
3)
Regression analysis will be used to determine appropriate
models
for
the accidents,
injuries and
fatalities
in the
different regions of Saudi Arabia and also for Saudi Arabia
overall, for a given set of regressor variables.
12
4)
Time
series
analysis
procedures
will
be
used
to
find
appropriate autoregressive moving average (ARMA) models for
the monthly accidents,
injuries,
and fatalities
in Riyadh
region and overall Saudi Arabia for 12 years,
and to
daily data of Riyadh area for about two years.
Theoretical
consideration of ARMA models
will be
the
introduced in brief
notes.
5)
Some
assessment
will
take
a
place
of
how
much
risk
is
involved in motor vehicle accidents and some recommendations
will be given of how they can be reduced.
13
CHAPTER II
LITERATURE REVIEW
2.1
INTRODUCTION:
It has been reported in the past few years, and in various
meetings and conferences dealing with the problem of Road Traffic
Accidents (or Motor Vehicle Accidents) that a great deal of the
deficiencies in research might be referred to the lack of statistical studies and analysis.
Such deficiencies make it impossible
for many developing countries to obtain valid and reliable data on
the magnitude of their motor vehicle accidents problem.
A fuller realization of the problem of road accidents is
required,
and
of
the
many
factors
which
contribute
to
road
accidents, before effective measures can be applied to alleviate
the present situation.
but
also a
far
It needs not only a coordinated approach,
more
effective
working
partnership
among
the
Police, Legislators, Educationers, News media, Engineers, Planners
and Doctors, and at the end, with the individual citizen.
Road
traffic
accidents have
Arabia within the past few years.
increased
steadily in Saudi
As a result of these accidents
many deaths, as well as permanent disabilities have occurred in
the past 10 years.
Some statistical information show a yearly
increase in deaths that might be compared to cancer and social
•
problems, Malaika (1983).
Most risks of accidents arise during the course of the day
particularly
at
night,
during
wet
weather,
and
adjacent
to
14
crossing facilities, and junctions are the most frequent sites of
accidents in urban areas.
The road traffic accidents in Uni ted Kingdom for 1985 are
251424 corresponding to
21
million
vehicles
320819 injuries and 5342 fatali ties.
Kingdom is about 56.5 millions.
injuries
and
fatalities
The
vehicles
accidents,
for
Saudi
in
The population of United
per 1000 vehicles
to
be
11.97,
United Ntions (1985).
injuries
Arabia
resulted
9ne can calculate the accidents,
rates
15.28, and 0.25 respectively.
and
in
and
fa tali ties
1985
are
700,
rates
5.5,
per
and
1000
0.8
respectively.
So the accidents and injuries rates in the United Kingdom
are greater than those for Saudi Arabia, but the fatalities rate
in Saudi Arabia are much greater than the same rate for the United
Kingdom.
Road accidents have become a major problem in most countries
of the world and have increased in developed countries to such an
extent
that roughly quarter of a million deaths and 10 million
injuries could occur annually On the world's road system within
the
next decade unless
very dramatic
steps
are
taken in many
fields of driving, to rectify this situation, Hobbs (1979).
World Health Organisation Statistics (1976) reveal that" in
developing countries over a third of all accident deaths are now
attributable to motor vehicle accidents.
The highest proportion of all accidents are caused by road
traffic accidents, Greenshield (1973).
15
The
Arabia
problem of
is
a
road
contemporary
traffic
accidents
one.
Epidemiological
certainly necessary for its control.
formed
in Saudi
in a number of countries
to
studies
Organizations
are
have been
study in detail different
aspects of traffic accidents.
The existence of complete statistical information is very
necessary in order to serve as a basis for evaluating related
activity
or
severity
and
even
for
frequency
preparing
of
road
a
logical
traffic
plan
for
accidents.
reducing
In
most
countries, police reports are the main source of information about
road traffic accidents.
According to Aaron and Strasser (1966), the component parts
of the traffic accident problem are indentified as,
the highway, and the vehicle.
Each of these are closely rela ted
to theories of traffic accident causation.
the most important
factor
the driver,
in the
cause
The human element is
of
traffic
accidents.
Mainly, such accidents are due to driver failure, carelesness, or
violation of man-made laws or laws of nature.
Estimates from
several studies indicate that the human element is responsible for
80 - 85% of all traffic accidents.
To
reduce
the
frequency of
road
traffic
accidents,
Lay
(1978) has suggested some recommendations such as: Prevention of
alcoholism and rehabilitation of alcoholics and softening roadside
hazards.
Safety campaigns should include components directed
specifically to groups represented in the accident statistics.
In
developing
countries
various
investigations
traffic ·accidents have been carried out and
of
their causes
road
and
consequences, as well as proposed preventive strategies, have been
studied.
'6
There are many factors which have an effect on the driver
and on his driving and likely involvement in an accident (or at
,
least in the severity of the accidents) such as age, attitudes,
driving
experience,
economic status,
psychological
status,
occupation,
level of education, driving
licence,
socio-
following
the traffic regulations, residence and income, and so on.
2.2
ACCIDENT CAUSATION:
Generally occurrence of accidents
is attributed not
to a
single cause but to combined causes of a number of factors
failures associated with the driver,
layout.
the
vehicle and
the
or
road
The errors which lead to road traffic accidents mostly
arise from behaviour often associated wi th some· driver deficiency
rather than from irresponsibility or deliberate aggression.
"Speeding undoubtedly is a major cause of accidents
victimize many innocent persons.
that
The faster the car is going the
shorter the time available to the driver to react and stop.
This
places him in a critical position when he has to stop suddenly.
The speeding is only due to the driver.
It is not confined to one
group as opposed to another but it is more prevalent among young
drivers.
I believe that counseling, education, and explaining the
problems that result from speed will have a positive effect of
them and convince them to reduce their speed, and encourage them
to observe the speed both inside and outside city limits.
will
reduce
the
number
of
accidents
and
resulting
This
injuries",
AI-Gattan (1986).
In considering the causes of road traffic accidents,
there
are three basic factors involved, human, road and vehicle . . Human
factors 'incorporate all factors associated wi th man:
psychological
experience,
and
physical
attitude,
and
characteristics,
other
such
behavioural
(1973), Mc Farland (1973) and Havard (1973).
his soc~al,
as
.
his
factors,
,
age,
Norman
17
The human factors which have been found to be consistently
associated with motor vehicle accidents are drinking,
speeding,
physical
and
psychological
fatigues,
excessive
and
specific
physical disabilities such as visual and sensory defects,
Havard
( 1973) .
Age is one of the socio-economic factors and has been found
in some studies to be one of the highest correlates of accident
envolvement
and
also
when
kilometers· driven
are
taken
into
account, Forbes (1972) and Mc Guire (1976).
It has been revealed in a study by Transport Road Research
Laboratory (TRRL), (1971) that hUman factors are a main reason in
65% of the cases and a contri butary cause in 95%.
More than one
quarter of the accidents studied displayed a deficiency in the
road
environment
linked
to
a driver error.
Mistakes
made
by
drivers and their difficulties in negotiating the road system are
useful indicators of faulty road design.
According to WaIler
& Hall (1980), and Hulbert (1976), the
accident involvement decreases as the driver's level of education
increases.
Mc Guire (1976) found that motor vehicle accidents are more
frequent
during
the
first
three
or
four
years
of
driving,
18
regardless of age, and drivers with formal driving training tend
to have fewer accidents and convictions than those who learn to
drive in other ways.
Mackay
(1967)
showed
in
a
detailed
study
in
the
United
Kingdom that driver error is wholly or partially responsible for
85% of accidents.
Conversely
caused relatively few accidents,
the
environment
and
less than 5% each,
the
vehicle
when acting
independently or in combination.
In a
three years study of fa tal
States of America it was
accidents in the United
shown clearly that
a majority of
the
dri vers who cause fa tal accidents have suffered more from severe
social stress and acute personality and psychiatric disorders than
other drivers, Doege and Levy (1977).
In Germany, France, Austria, Switzerland and the Netherlands
alone the deaths from road traffic accidents account for nearly 4%
of all deaths and 50% of deaths are among young males between the
ages of 15 countries
24.
is made
The comparison of accident statistics between
difficult because common definitions
are
not
used, Hobbs (1979).
Among factors associated with the increase of road traffic
accidents were thought to be the greater power of the vehicles
involved,
an
increased
number
of
heavy
goods
vehicles,
and
advances in techniques of medical resuscitation meaning that even
the most seriously injured may survive, W.H.O.
(1976).
19
In the United states the age group 16 - 24 years contains
22% of the driver population, but is involved in 35% and 39% of
fatal and all injury accidents respectively.
Overall,
sexes,
35 years of age,
the accident rate is lowest from 30 -
for both
Hobbs (1979).
According to River (1980), old drivers have longer reaction
times than do young drivers.
reaction time
begin to
At about forty years of age, simple
increase to
the
extent
that at
about
seventy years of age, a driver's reaction time may increase by as
much as 50%.
Strong associations have been found in the incidence of the
motor vehicle accidents between the young,
and the older experienced drivers.
inexperienced drivers
The older and
experienced
drivers were found to be infrequently involved in motor vehicle
accidents
and
minor, W.H.O.
when such
accidents
occurred
they
were
usually
(1966), Norman (1973), Mc Guire (1976) and Forbes
(1972).
The type of road travelled by motor vehicles has been shown
to be associated with motor vehicle accidents.
include ditches
on
roads,
confusing road
surfaces, Doege and Levy (1977).
signs
These factors
and
poor
road
20
2.3
ACCIDENT REPORTING:
Accident analysis depends on the completeness and accuracy
of the accident reporting.
Because trends have to be interpreted,
and significant changes detected from control and design measures,
consistency in methodology is necessary for the effectiveness of
improvement
to
be
scientifically
evaluated.
It
must
be
appreciated that there are generally a large number of variables
present in accident analysis.
The
total
accident
recording the number of
picture
accidents
is
most
easily
obtained
over several years
and
by
the
factors involved, and the number of vehicles registered from year
to year.
This
information can be
used
not
only
to
estimate
further growth, but also to help plan new roads and new traffic
policies,
(Department
of
Scientific
and
industrial
Research,
Research on Road Safety), (1963).
Accident statistics
research
since
they
are
supply
the main concern of
basic
information
road
safety
concerning
the
relative importance of the various factors which contribute to
accidents.
This information' is often used as a guideline and
method of preventing road accidents and to assist in determining
the direction of further investigation, Saif (1973).
In Great Britain the police authorities are the body responsible for accident reporting and the compilation of records.
Similar systems are adopted either wholly or in a modified form in
many countries of the commonwealth, Hobbs (1979).
21
But
in Saudi Arabia
the
General Department
of
Traffic,
Ministry of Interior, is the only responsible body for recording
and
reporting motor vehicle accidents and publishing the
data
which are directly related to traffic and road traffic accidents.
Statistical data on road traffic accidents are required for
law enforcement and the distribution of manpower for surveillance.
Unfortunately the initial recording of the factors involved in an
accident lies solely in the hands of the reporting police officer
whose judgement in these matters is necessarily limited by the
extent and nature of his training, Hobbs (1979).
Accident
incomplete.
accident.
reporting
in
Saudi
Arabia
was
found
to
be
Police reports are prepared for two categories of
The first category involves fatalities and injuries, if
and only if a liability issue is involved.
For ins tance, if an
accident involves one overturned vehicle resulting in the death of
the driver,
this would not be
recorded in the first category
because there is no liability at
issue.
The second category
involves a few cases' of property - damage only type accidents
where
the dispute has
not
been
involved at the accident site.
resolved
between
the
parties
The available statistics that are
published yearly by the Ministry of Interior are a summary of the
accidents in these two categories, Al-Khaldi & Ergun (1984).
A study by Bull and Roberts (1973), suggests that between
one-sixth and one-third of slight injuries do not appear in the
police
re~oting,
records.
Because of this
possible bias due to under-
the analysis in the study concentrate on fatal and
serious injury accidents.
22
Of course there is not a typical form for- the accident data
and r-ecor-d keeping for overall the world.
To make the compar-ison
of accident analysis between two or- more than two countr-ies, it is
necessar-y to take account of societies cultures which differ- from
country to country.
Population, fatalities from r-oad accidents, and numbers of
vehicles were used as the basis for the study of international
comparisons of r-oad accident statistics and it was found that the
risk
to
country.
published
pedestrians
and
the
risk
to
car
occupants
varies
by
Comparisons could be precise if statistics were
in more detail and with uniform criteria in all
countries, Bull and Roberts (1973).
2.4
THE PROBLEM IN SAUDI ARABIA:
Many studies regarding accident analysis and
prevention of
road traffic accidents have been carried out locally and internationally.
In the Kingdom of Saudi Arabia statistical analysis
of road traffic accidents r-esulting in injuries and fatalities are
reported by. some investigators.
traffic accidents represent
Mufti
(1983),
said
that
road
the second major medical problem in
Saudi Arabia after infectious diseases.
He discusses the effects
of road traffic accidents, using the results of studies that were
carried out in Riyadh and other parts of Saudi Arabia.
Analysis of the available data during the period (1971-1980)
includes comparison with the study of figures from the U.S.A. and
According to Saudi stipulations, a road traffic accident is
defined as that which is caused to or by a moving vehic le and
which results in a fatality or bodily injur-y, or damage to or loss
of property.
Excluded from the above definition are deliberately
inflicted acts that fall within the domain of criminali ty under
the penal. code of Saudi Arabia. Also excluded losses or injuries
r-esulting to or from vehicles parked in authorized ar-eas.
"
23
Bener et. al. (1988) have made an epidemiological study of
road traffic accidents in Riyadh, the capital city of Saudi Arabia
in the period· of 1974-1985.
The figures of accidents, injuries
and fatalities rates are compared with the same figures in Kuwait.
There are 1.9 cars
for each family in Riyadh and 38% of all
involved drivers in accidents in Riyadh are unlicenced drivers.
AI-Thenayan (1983) reports that in Riyadh the drivers in the
age group of 21-25 are the most frequently involved group with
26.6% of accidents, when compared to other age groups.
Nearly 83%
of the accidents involved drivers who were 34 years old or less.
AI-Khaldi and Ergun
between characteristics
economic
investigate
the
relationship
(which are represented by
characteristics
accident involvement.
(1984),
and
some
attitudinal
some
socio-
questions),
and
This study used a sample of roadside inter-
views carried out in the Eastern Region of Saudi Arabia.
Analysis of variance and covariance, multiple classification
analysis,
and
relationships.
main
variables
regression
analysis
are
used
to
analyze
the
The analysis using these techniques isolates three
as
significant.
occupation, and income.
These
variables
are
age,
All other variables become insignificant
when the effects of these variables are taken into account.
2694 road traffic accidents in six major hospitals in Asir
Province for the years (1975-1977) were analyzed in a study by
Tamimi et. al. (1980).
driver error.
Almost 97% of the accidents were due to
50% of injuries from the accidents were to people
between 20-40 years of age.
accidents.
82% of the deaths were due to road
24
AI-Y~aldi
and
evidence
that
Ergun
(1984),
psychological
show
in
variables would
their
be
study
useful
some
the
i~
predic;tion of accident involvement and possibly in the formulation of measures to correct driver behaviour.
At
the
Riyadh
Central
1500-2000 patients
Hospital,
admi tted yearly because of chest injury.
are
This figure constitutes
approximately 15% of the casual ties due to -road traffic accidents,
Hamdy (1 982 ) •
Malaika
(1983)
suggested
established in major cities
that
to
portation of the injured patient.
trauma
centres
should
improve the methods
be
of trans-
Need is stressed for the prompt
treatment of victims of traffic accidents in Saudi Arabia.
Data
regarding
cause,
age,
sex,
nationality,
seasonal
variation, management and outcome of 1285 cases of head injury
between
the ages
of 15 and 30 years
are
presented.
It
is
concluded that in Taif road traffic accidents are the commonest
cause of head injury in persons in their teens and twerities with a
high rate of mortali ty, Khan and 110hiuddin (1982).
During 1979. 28271 cars were involved in 17743 road traffic
accidents in Saudi Arabia.
2871
people and
the
These accidents led to the death of
hospitalization
of
16832 patients.
The
average period of hospi taliza tion for each ps tient was 15 days.
!1ore than 60% of patients were between 15 and 45 years of age.
40% of these accidents occurred in the Riyadh area.
calculated
that
the
country
loses approximately 4776836
Riyals per day due to road traffic accidents ( £1
Riyals), Kawasky (1980).
It
is
Saudi
... 6.0 Saudi
25
Bener and El-Sayyad
(1985)
revealed the magnitude of the
problem during six years in Jeddah,
Saudi Arabia in the period
(1978-1983), and examined some epidemic aspects of road traffic
accidents.
The following facts have emerged:-
factor of excessive speed 66%.
d ri vers
aged
18-30
invol vement 36%.
made.
46%
and
There is a high
High percentage of non-licensed
high
percentage
of
pedes trian
Recommendations to improve the situation are
26
CHAPTER III
DATA REPRESENTATION
3.1
INTRODUCTION:
Data
representation is
statistical analysis.
considered
In the field
as
a
basic
step
in
any
of road traffic accidents it
appears to be a very important .elementary indicator on the accidents
position.
Carefully presented, such representation can be important
in providing elementary indications of the changing levels of road
traffic accidents and their consequences.
The
General
publications
Directorate
(Yearly
of
Statistical
Traffic
Book)
collecting the data in Saudi Arabia.
in
is
Riyadh
the
it's
source
on
It is the main source of our
dsta of the accident variables in the different
Arabia,
only
and
except. the daily data of Riyadh area,
regions of Saudi
which is collected
manually from the accidents records from the Traffic Department of
Riyadh.
In
this
chapter
we
discuss
available data and it's sources.
the
different
kinds
of
the
The data falls into three groups.
The first is the daily data, which is available for approximately
for two years, secondly the monthly data for 12 years and finally
the yearly data for
years.
1~
The later kind of data is
analysis in the next chapter.
period and all
the
the main part of our statistical
Because it is available for a long
related variables
(like population,
number
of
issued driving licences, types of imported vehicles) are given year
by
year.
The
other
two
kinds
of
data
include
only
number
of
accidents, injuries, and fatalities.
In the following we will discuss in brief these three kinds of
data with some basic statistics.
Simple graphs, like the histogram,
give a good idea about the properties of these variables.
27
3.2
DAILY DATA:
This
is the first kind of data which
sequence of 708 days in the years 1982 and 1983.
is
conaiderE!d as
a
The data are taken
from the traffic records which are available for Riyadh area only.
which is different than Riyadh region. where Riyadh area is a part
of Riyadh region.
Each observation consists of the following:
1 -
The day number (DAY). which is from the day number 001
to the day number 708
2 -
The accidents (ACC). the total number of road traffic
accidents on each day
3 -
The injuries (INJ). the total number of injuries which
result from these accidents.
4 -
The fatalities (FTL). the total number of fatalities
which result from these accidents.
Table (3-1) gives the full information of the first kind of
data.
Some basic statistics about these variables are given in Table
(3-2) •
From Table (3-2). we note that the correlation coefficients(r)
between these variables are small.
except between accidents
and
injuries which is 0.49. accidents and fatalities are uncorrelated
( r
=
0.01 ). In the next section we will give a reason for this
small value.
The frequency table for the accidents. injuries and fatalities
in
the
Riyadh
respectively
~ith
area
are
given
in Table
(3-3). to
its corresponding histogram.
Table
(3-5).
28
3.3
MONTHLY DATA:
The data of 144 months (12 years) in the period of 1974-1985
are available for Saudi Arabia and its six regions.
Each observa-
tion contains the following:
1 -
Month (M) which is between 001 and 144.
2-
Accidents (ACC), the total number of road traffic
accidents on each month.
3 -
Injuries (INJ), the total number of injuries which
resulting from the accidents in the month M.
4 -
Fatalities (FTL), the total number of fatalities which
result from the accidents in the month M.
It is not practicable to include all the data of Saudi Arabia
and
its
regions,
Riyadh region,
so we will
include the
data
of Saudi
Arabia,
and Makkah region, because they represent the main
regions of the country and include the major part of the accidents
injuries and fatalities.
The data are
given in Table
(3-6)
to
(3-8), respectively.
Some basic statistics of this kind of data for Saudi Arabia,
Riyadh region and Makkah region .are given in Tables (3-9)
to (3-11),
respectively.
The
correlation
strong correlation.
coefficients
between
these
variables
show
There is a big difference in the correlation
coefficients between the daily data and the monthly data for the
Riyadh region and this could be due to the stability of monthly data
rather than the daily data and the degree of accuracy of the daily
data is less than the monthly data.
It may be happen that
some
fatali ties or injuries of an accident are recorded in the next day
or after few days rather than the corresponding day, which is a form
of recording deficiency in system.
Plots of accidents, injuries, and fatalities against the month
for Saudi Arabia and its different regions are given in Fig. (3-1)
to Fig. (3-7).
29
3.4
YEARLY DATA:
It is the main body of data which consists of annual data in
the period of 1971-19B5, i.e. for 15 years.
data before 1971.
There is no available
After 19B5 data does not exist at the time of
preparing this study.
The data is listed under ten variable headings:1-
2345678-
910-
Number of road traffic accidents each year (Yl).
Number of injuries resulting from road traffic accidents each
year (Y2).
Number of fatalities resulting from road traffic accidents
each year (Y3).
Population size based on estimation as given in Appendix A
(Xl) •
Accumulated number of registered vehicles upto the given year
(X2) •
Number of newly issued driving licences each year (X3) •
Number of newly registered transport vehicles each year (X4) •
Number of newly registered private vehicles each year (X5) •
Number of newly registered taxis each year (X6) •
Number of newly registered buses each year (X7) •
These variables are given for the six regions of Saudi Arabia
and Saudi Arabia overall.
The seven parts of the data studied here
are as follows:
1-
23-
4567-
Saudi Ara bia overall (SAA) •
Riyadh region (RYH) .
Makkah region (MKH).
Dammam region (DM,) •
North region (NRT) •
Qaseem region (QS!t.) •
.
South region (SU~)
The data of these regions for the above variables are given in
Tables (3-12) to (3-1B).
30
The data are taken from the General Directorate of Traffic in
Riyadh, Saudi Arabia (Yearly Statistical Book); but those pertaining
to population are based on estimation as in the Appendix (A).
Some basic statistics of this data are given in Table (3-20)
to Table (3-26).
3.5
CO~ENTS
AND DISCUSSION:
To
form a
good
idea regarding the high rate of accidents,
injuries and fatalities in Saudi Arabia and its different regions,
let us take two years, 1973 and 1983, giving an interval of
ten
years, and construct histograms for of these variables as given in·
Fig. (3-8).
By referring to the data which relate to Fig. (3-8), we note
that the number of accidents,
injuries,
increasing steadily at a high rate.
and fatalities have been
These figures are summarized in
Table (3-19).
We
grea ter
note
from
Fig.
(3-8)
that
than the number of injuries
the
number
only for
the Southern region, and Saudi Arabia overall.
of
accidents
is
the Riyadh region,
In the other regions
we find that the number of injuries are more than the number of
accidents. On the other hand the accidents in the Riyadh region and
in the Southern region are less severe than in other regions, as is
clear from Table (3-30) and Table (3-31).
We will
discuss in detail
the si tua tion in the Riyadh and
Makkah regions in 1983 as given in Fig. (3-8), because these are the
two main regions in Saudi Arabia.
31
In the Riyadh region,
during the period of
(1971-1985)
the
number of accidents is three times that of the resulting injuries
from these accidents, where we have 36 injuries per 100 accidents
and about 4 fatalities per 100 accidents.
In the Makkah region, the number of injuries is greater than
the
number
of
accidents,
where
there
are
133
injuries
per
100
accidents and 18 fa tali ties per 100 accidents.
The difference between these two regions is attributed to many
factors, some of which are:
1-
The population of Makkah region in 1983 was 2329012, which is
greater than the population of Riyadh, which is 1689259.
In
addition the Makkah region includes three big cities in Saudi
Arabia, which are Taif, Makkah, and Jeddah, while the Riyadh
region has only one big city which is Riyadh City.
2-
There is not a big difference between the number of registered
vehicles in the two regions.
There are 1160663 vehicles in
Riyadh and 1194933 vehicles in Makkah, but a difference exists
among
the
t rans port,
four
types
taxis,
of
and buses.
vehic les,
Whereas
which
are
in Riyadh
pri va te,
region
the
percentages of these types of vehicles in 1983 are 54%, 45%,
0% and 1% respectively,
in Makkah region the percentages are
57%, 43%, 0% and 0.06% respectively.
3-
Hajj
season in
for
~!akh,
two
to
three
weeks,
every year
during which more than two million muslim pilgrims arrive in
the Hakkah region from all over the world.
effect on increasing the number
of
injuries,
pilgrims
and
transportation
fatalities.
and
this
rates per 100 accidents.
Most
increases
road
the
This has a major
traffic accidents,
use
the
injury
and
buses
as
fatality
32
In
the
Hajj
season
of
1993
there
were
1003911
pilgrims
arriving from outside Saudi Arabia, and 1497795 arriving from
inside the country
a total of 2501706 pilgrims.
About 333000
vehicles entered 11akkah in this short interval.
In the monthly data of Makkah region in 1983 there were 638·
traffic accidents,
1057 injuries,
and 162 fatalities
during
the
mont" of Hajj.
The same figures for the same month for the Riyadh region were
802 traffic accidents, 354 injuries, and 38 fatalities.
According to the number of vehicles one can easily calculate
the accident rate per 1000 vehicles (ARV), the injury rate per 1000
vehicles (IRV), and the fatality rate per 1000 vehicles (FRV).
The calculation of these rates for all the yearly data are
given
in Table
(3-27)
to
Table
(3-29),
by
using
the
following
can
find
relations.
ARV
IRV
FRV
=
=
(1)
(ACC/VHC) 1000
(INJ/VHC) 1000
(FTL/VHC) 1000
According
to
the
number
( 2)
(3)
of
accidents,
one
the
injury rate per 100 accidents (IRA) and the fatality rate per 100
accidents (FRA) by the following relations.
IRA
= (INJ/ACC) 100
FRA
=
Applying
(4)
(5)
(FTL/ACC) 100
these
relations
to
the
regions and for Saudi Arabia overall,
in Table (3-30) and Table (3-31).
yearly
data
for
the
six
these calculations are given
..
Table
(3-27)
33
indicates
that
the
accident
rate
per
1000
vehicles decreased year after year, and this can be attributed to
the increase in the number of vehicles in the country On the other
hand ,. the number of accidents is still increasing, but the increase
in the number of vehicles is much greater than that of accidents.
For Saudi Arabia on the average there are 18 accidents per
1000 vehicles during the period of study (15 years).
The Southern
region has the greatest accident rate, an average of 54 accidents
per 1000 vehicles.
vehicles
in
difficul t ,.
that
because
This could be attributed to the low number of
region
it
and
to
contains
the
the
nature
highest
of
the
mountains
terrain
in
is
Saudi
Arabia.
The injury and fatality rates per 1000 vehicles ( given in
Table (3-28) and Table (3-29)) vary over the different regions with
the Southern region having the highest average, which is 70 injuries
and 10 fatalities per 1000 vehicles.
The Riyadh region has the lowest rate, averaging 10 injuries
and one fatality per 1000 vehicles.
This is due to the high number
of vehicles, where in 15 years (1971-1985) the number of vehicles
increased from 67607 to 1297007.
The figures for the Southern region is qui te different where
the number of vehicles increased during the same period from 1795
to 197983.
The injury and fatality rates per 100 accidents are given in
Table (3-30) and Table (3-31).
Over a period of 15 years there were
85 injuries and 13 fatalities per 100 accidents in Saudi Arabia.
34
Of
all
the
different
regions,
the
Qaseem
region
has
the
highest record in injury and fatality rates, with 136 injuries and
26 fatalities per 100 accidents.
At the other end of the spectrum
the Riyadh region has the lowest injury and fatality rates, with 43
injuries and 4 fatalities per 100 accidents.
Fig. (3-9) and Fig. (3-10) give a summary of these rates.
According
to
the
population
size
(pop)
one
can
calculate the accident rate per unit population (ARP) ,
rate
per
population
unit
population
(FRP),
where
(IRP)
and
the unit
the
fatality
population is
easily
the injury
rate
per
considered
unit
to
be
10000.
The above
different
rates
regions
are
calculated
of Saudi Arabia
for
and
the yearly
data
given in Tables
of the
0-32) to
(3-34) by using the following relations
Our
ARP = (ACC / POP ) 10000
(6)
IRP = (INJ / POP ) 10000
(7)
FRP
(8)
concern
(FTL / POP) 10000
is
to
look
for
the
relationship
between
the
different regions and the different rates per unit population in a
period of 15 years (1971-1985).
Two way analysis of variance, ANOVA,
is used to see if there
are any differences between the regions and between the years for
each of the above rates.
This can be done by building the ANOVA
table for each ra te and calculating an F-value for the years,
for the regions.
and
35
Before carrying out the ANOVA we will check the given rates to
see whether the usual normality assumptions hsve been met.
This can
be done by obtaining a histogram showing the distribution of each
region.
From these histograms we note that the given rates are not
normally distributed and need to be transformed.
Another check on the
above rates
is made by plotting the
standard deviations of all the regions against their means and then
plotting the variances of all the regions against their means for
each rate.
The
above
two
plots
reveal
that
the
given rates are
log-transformation of these
rates
not
normally distributed.
The
is
sui table in this case.
The transformed rates are given in Tables
(3-35) to (3-37).
The corresponding ANOVA tables for the accident, injury and
<
fatality
rates
per unit
population after
log-transformation
are
given in table (3-38).
The F-values due to regions and due to years are both very
highly significant for each of the above three rates.
conclude that there is a real difference
We therefore
between the regions, and there is a difference between the years for
toe logged accident ,injury and fatality' rates per unit population
as indicated by the above analysis.
In what follows, we shall look to the regions to Bee which
ones are essentially different in this respect, and which ones are
similar.
this
The same procedure will be followed for the years.
reason
we
shall
apply
Duncan's
Multiple
Range
Test
For
for
comparing the set of 6 means representing the six regions with equal
size 15, and comparing the set of 15 means representing the 15 years
with equal size 6.
36
Then we shall consider the means in sets of size P. Bay. for
values of p ranging from 2 to 6 for the regions and ranging from 2
to 10 for the years.
magni tude.
The means are arranged in ascending order of
The least significance range for the difference between
the p means is
where rp is obtained from tables of Duncan' s Multiple Range Test
and HSE is mean square error.
We consider the means in sets of 2. 3 • ••• • 6 at a time for
the regions and in sets of 2. 3. '"
• 10 at a time for the years.
Then we underline the sets of means with a range less than Rp for
each value of p.
We underline sets of means which are alike. for in
this way we can decide which of the means stand out from the rest.
The test procedures of Duncc)n' s multiple range test for the
given three
rates and
the
six regions are
summarized in tables
(3-39) to (3-41) at 1% and 5% risk.
The test procedures of the above test for the given three
rates and the 15 years are summarized in Tables (3-42) to (3-44) at
5% risk.
In the following we shall present conclusions about each rate,
according
to
multiple
Dun~'s
range
test.
In
each
case,
the
comments refer to the log transformed data.
For the accident rate per unit population:Differences exist between all the regions except for the set
of
the
North
and
Dammam
regions
(at
0.01
and
0.05
level
significance) and the set of the Qaseem and North regions (at 0.01
of
.
37
level
of
significance).
Those
regions
which
do
not show
a
significant difference are underlined in Table (3-39).
The yearly means are increasing with years, as expected, and
the largest increases occur in the early part of the period under
study - in particular, between the yearS 1971 and 1972.
The years of the period 1975-1982 reveal that any differences
between them are not significant at the 0.05 level of significance.
Test procedures are given in table (3-42).
For the injury rate per unit population:Again, differences exist between the regions, except for the
sets of the Qaseem and North regions, the North and Dammam regions
and
the
Riyadh
significance).
and
Makkah
At
the
regions
0.05 level
(at
of
0.01
and
0.05
significance
level
there
difference in the set of the Qaseem, North and Dammam regions.
is
of
no
Test
procedures are given in Table (3-40).
For the years,
level of significance.
1971,
years.
there is a difference between them at 0.05
This can mainly be attributed to the year
which again stands out as different from the
remaining 14
There is no appreciable difference in the yearly means in
the period 1978-1985 (if we take the years as a set of 8) and in the
period
of (1972-1977)
(if we take the years as a
set of 6) as
described in Table (3-43).
For the fatality rate per unit population:There is a very clear difference between the regions, except
in the following sets of regions: the Qaseem and North regions and
38
the Dammam and Makkah r~gions
(at 0.01
and 0.05 level of. signi-
ficance) and the Riyadh and Qaseem regions and the Riyadh, Qaseem
and North regions (at 0.01 level o~
significance) as described in
table (3-41).
Also, there is a difference between the years at 0.05 level of
significance.
No difference exists between the years of all the
sets of two years.
Again there is no difference between the years
1976, 1978-1985, (if we take the years as a set of 9) as explained
in table (3-44).
Finally we conclude that
the Dammam and North
regions
alike for the accident and injury rates per unit population.
Dammam and Makkah
regions
are alike
in
the
fatality
rate.
are
The
In
general, we can conclude that the differences among the six regions
cannot be attributed solely to one or two regions, but each region
contributes to this difference.
There are other variables concerning accident statistics that
are not included in this chapter, but are available in the Yearly
Statistical Book of the Traffic Department.
This data can be divided into two main parts.
the number of road traffic accidents
First, there is
tabulated according to many
factors such as day of the week, time of the accident, day or nieht
and type of accident.
Second,
the number of drivers involved in
road traffic accidents are classified according to age, nationality,
education level, and possession of a driving licence.
But all these data are given for a short period,
only 8
observations
for
each
variable.
This
is
BO
we have
therefore
not
suitable for the model fitting procedures by regression analysis or
time series analysis.
Table (B-1)
DAY
IN-l
ACC
The daily accidents, injuries, and fatalities of Rlyadb:
FrL
DAY
ACe
INJ
FTL
DAY
ACC
INJ
FTL
for
1982 -
DAY
ACC
1983
INJ' ,FTL
DAY
,
31
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
11,
17
18
19
20
26
23
12
'
19
39
35
, it,
30
32
22
32
"
7
11
5
7
4
4
11
4
7
3
10
9
3
26
16
42
23
29
11
1'1
21
22
23
-0
,',',
:J4
22
:~5
25
25
26
27
14
10
12
6
6
4
11
14
33
37
2!?
3
o "
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
:2
0
22
7
14
3
76
77
78
79
00
81
6
33
6
37
17
f,
38
28
9
39
40
41
27
14
34
10
27
45
30
'I
.2
5
10
7
10
0
0
0
4"
45
46
47
48
4'1
50
51
52
53
54
55
'7
9
6
7
"4
3B
El
"-,
.::..:..
5
5
39
28
fJ
6
10
25
27
30
:~
"
10
3
11
1
19
26
--- -~
35
3
2
1
1
0
3[,
43
73
20
33
34
, 35
42
27
35
34
20
22
23
23
39
29
11
7
6
8
7
31
32
22
75
25
37
22
25
29
20
30
62
63
64
65
66
67
60
(,9
70
71
72
74
1
2
0
1
2
1
0'
0
1
1
0
1
28
29
1,1
27
24
55
33
33
26
31
30
0
"
213
2tl
20
56
57
58
59
60
6
1
0
0
0
0
0
0
1
0
2
0
0
8~'
83
84
85
86
87
88
89
90
91
92,
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
22
23
34
29
22
23
25
32
37
27
23
7
9
11
11
9
6
1
0
1
1
6
1
13
3
B
0
,4
10
5
10
6
6
3
5
13
10
7
10
5
3
1
0
0
2
2
0
0
<1
10
10
5
9
4
11
9
8
6
2S
10
19
37
21
2S
45
7
30
36
25
28
35
6
3
"
10
11
B
26
28
27
10
11
5
5
5
i 4
3
4
6
4
31
6
36
24
12
36
26
37
18
21
16
13
6
4
0
1
1
0
1
0
0
1
1
2
2
2
1
0
0
1
0
0
2
1
0
3
2
1
1
4
0
1
0
1
3
0
()
1
0
1
0
"
0
1
111
34
112
23
113
114
115
116
117
118
119
120
130
131
1 :32
133
134
22
36
35
22
17
41
28
::!9
29
15
20
25
:11
32
33
22
29
:16
35
31
29
32
135
29
136
137
138
139
140
141
142
143
144
145
146
147
148
149
34
121
122
123
124
125
1:26
127
12B
129
150
151
152
153
154
155
1 ~)6
157
23
30
29
35
:16
39
43
40
35
20
37
44
35
30
14
25
48
4.
25
29
17
43
158
159
25
160
161
162
38
29
29
11.,3
164
1115
:10
27
·10
5
5
7
16
7
10
8
11
6
12
11
6
9
7
5
11
5
7
8
10
2
14
11
4
12
9
12
B
"
7
8
I,
17
15
12
5
8
11
6
•
10
B
9
14
11
9
4
13
14
9
7
9
0
1 bb
7
1
0
1
0
3
2
0
1
0
2
167
160
169
170
171
172
173
174
175
0
2
2
2
0
0
0
3
1
7
1
1
0
2
3
0
0
0
0
0
2
5
0
1
0
0
0
0
1
2
3
1
()
0
0
0
176
177
17B
179
180
181
19
36
24
21
35
35
29
32
26
26
12
31
29
34
32
21
182
25
183
184
43
27
38
20
1 B5
186
107
188
1(19
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
2~5
43
30
36
44
213
6
214
0
1
0
215
216
217
9
6
0
~1a
0
9
1
211J
220
.4
0
2
0
0
0
0
1
1
0
9
0
4
6
14
11
10
14
12
9
7
5
0
1
3
1
B
8
9
11
6
40
16
35
211
212
(1
4
8
9
6
6
5
4
222
223
224
23
19
36
40
42
35
32
27
17
30
28
30
21
38
209
210
221
0'
8
20tl
208
0
9
32
21
41
46
6
13
13
13
4
10
7
e
5
6 ,
5
7
9
10
6
10
12
10
11
35
9
5
6
1
5
7
9
34
15
26
21
41
15
33
::.
3
2
1
0
1
1
0
1
2
0
1
0
1
1
0
0
0
2
2
0
1
2
1
0
1
2
0
2
1
0
4
0
0
1
2
I
1
1
Ace
INJ
42
28
21
10
14
6
3
11
12
16
5
6
B
7
4
Fll
.
8
:~3
207
I
225
226
227
229
229
230
231
232
;!33
234
235
236
237
238,
239
240
241
242
243
244
245
246
247
248
249
33
45
46
64
13
21
34
42
27
3S
22
45
22
50
28
16
19
46
47
44
30
23
23
39
20
250
37
29
251
1J
252
253
17
36
29
30
22
15
254
255
256
257
258
259
260
261
262
263
264
265
266
267
26B
269
270
271
272
21
36
23
23
17
26
14
i 1
35
13
13
52
11
23
25
273
30
274
27
275
30
1
1
1
0
2
0
1
2
0
0
1
0
12
0
10
9
5
15
8
5
8,
11
10
10
5
7
2
1
1
2
4
2
1
0
0
0
0
2
'0
0
11
9
8
10
9
5
' 14
1
1
1
1
3
1
8
10
8
1
7
13
12
7
4
11
7
3
3
2
2
9
11
6
8
3
4
9
~
I
I
4
;!
0
1
1 ,
2
0
j
2,
0;
()
0
1
0
0
0
0
0
3
0
1
0
1
0
Table (3-1)
DAY
ACe
276
2T.'
278
279
2DO
2a1
202
2D3
2B4
19
:~B
25
43
33
23
22
3~)
207
22
i 9
23
25
2BO
2:~
2fFi
290
291
:':'1.92
30
33
17
2 fr'3
21
:'~9·4
295
27'6
14
33
23
:.~97
~,Il
2B5
2D6
'
25
IN~J
29
8
3()j
2B
302
40
36
29
9
3
:la3
304
-"
3()~>
30t)
307
30B
309
~o
16
35
23
46
310
2:>
:1 j 1
34
21
20
32
36
37
28
36
34
312
313
314
315
31t.,
317
:310
319
320
3.21
322
32:5
324
32~>
32b
327
:~28
329
330
:131
17
34
43
29
19
20
43
~!4
24
29
34
42
3:32
333
334
335
336
337
33[1
:539
340
341
~
22
:;~9
1
1
0
1
2
0
0
7
0
1
0
1
7
2
0
1
0
300
19
DAY
10
6
1,..,
9
10
9
6
9
10
10
5
2
16
3
8
10
8
4
10
B
1 ()
5
1
:~98
FTL
"
10
~)
4
4
1()
13
9
9
14
10
4
12
6
8
11
9
3
9
9
5
15
5
HI
5
4
6
:)
17
0
0
()
Ace
~!6
26
:20
26
11
13
11
2~)
~!O
350
20
36
34
3;!
29
34
35
24
3:1
40
1
3D
~
3'""
1
0
0
0
353
354
37
37
19
26
23
42
34
()
1
2
1
0
0
0
1
1
2
0
1
1
0
0
0
1
1
2
0
0
0
0
3
0
2
2
1
1
3
1
~.42
343
344
345
346
347
34B
34f}
3~)
.1 ...
35~)
356
357
350
359
360
31)1
362
31
2:2
;.~:
363
364
23
35
39
36~5
31
:566
~o
:~67
39
33
31.,B
369,
370
371
372
:373
374
:51'5
:n,l.)
37~1
378
379
380
3F11
3B2
:H13
384
385
3(J6
387
21
",.
....
)
21
38
34
29
36
31
40
4fl
30
59
:35
25
35
/'7
43
39
31
---
FTL
IN,J
9
8
4
6
5
3
3
11
8
6
15
2
'I
7
El
9
11
9
HI
4
16
6
8
7
3
1 ~)
:1
7
'7
4
10
,;
6
5
'I
13
10
6
10
1
1
1
0
0
2
4
3
1
1
3
0
1
2
1
1
0
0
°
0
1
0
'2
0
0
1
0
'2
'2
1
3
0
0
0
2
0
2
0
9
19
6
17
9
8
1 :1
, 10
2
0
0
3
1
1
1
0
6
1
1
1
0
1
0
1.6
0
'/
15
2
2
n
{,
B
11
11
n
DAY
Ace
:188
:189
:190
391
392
393
394.
395:
396
397
398
399
400
401
40~
403
404
405
40b
407
408
409
410
411
412
52
41
30
39
40
21
4()
42
4~=;
IN.!
10
15
11
7
1 ')
11
13
10
20
25
El
51
19
11
10
17
9
7
6
7
14
16
12
19
11
12
3t)
:51
47
30
17
31
:53
4f1
4'"'
50
~)7
:m
FTL
DAY
1
1
1
1
2
3
0
1
444
445
446
447
448
449
450
4~)
1
452
453
454
455
456
457
458
459
()
0
0
0
1
0
1
0
0
3
0
1
0
0
1
0
0
0
0
0
41/.)
417
3D
50
41
39
40
31
28
4111
3~i
4H'
36
4~0
421
33
40
422
3D
1':)
()
423
12
~124
38
34
425
4~
17
14
10
10
14
11
0
0
0
0
1
0
41:>
414
415
426
427
9
'I
11
'7
()
10
13
6
14
0
0
473
474
475
476
477
478
479
/,
50
430
431
432
33
4 :(:5
3B
1 ':)
434
435
436
437
43B
47
40
41
40
14
4:~9
24
:l3
30
:%
34
440
441
442
443
465
466
4/)7
468
469
470
471
47~!
429
3~)
4f.)4
()
42D
30
461
462
463
::>
Il
37
44
45
:.~(J
4ilO
1':)
()
1
3
0
1
1
1
0
4B0
4H1
4El2
483
484
485
4B6
1':1
0
9
13
11
()
b
0
9
1
407
·jOtl
409
490
491
4'72
49:5
494
495
496
Il
()
4(1'7
9
8
1
0
498
11
1
0
49~)
Ace
31
32
29
35
25
46
37
29
37
26
35
42
3()
31
34
22
21
48
27
38
22
56
28
16
25
40
32
28
39
35
25
37
31
28
32
2B
25
31
36
36
28
27
38
:~5
is
43
43
45
40
32
31
37
4()
43
33
42
continue
FTL
INJ
."
'7
10
12
1.0.
/,7
17
\3
'1"1
14
5
10
6
7
13
13
I>
6
10
8
9
6
18
12
8
4
14
9
10
4
11
10
11
4
7
7
11
10
12
9
7
5
6
13
8
'1
12
1~)
10
8
11
8
9
12
14
10
5
.
DAY
0'
2
0'
0
0
2
0
1
3
0,
1
1
0
3
0
1
0
ACC
:500
30
~}01
2~
502
503
504
:~4
506
507
508
509
510
511
512
513
514
515
516
44
23
30
34
36
40
2:)
45
43
28
35
32
29
'27
0
~)17
:,~9
0
0
0
6
0
0
0
1
0
1
~)1
0
1
0
'2
0
0
1
0
2
0
0
0
0
0
1
0
2
:1
0
2
0
1
0
0
1
1
0
0
505
523
524
59
34
23
23
23
11
24
~)25
3~1
526
527
528
529
530
31
31
32
8
9
~)1
~j20
521
522
531
5 7 '1
533
INJ
Fn,
14
9
10
16
11
I>
5
10
14
9
15
11
·9
9
9
9
11
8
9
'7
~)
4
II
5
5
6
5;34
31
5:55
411
12
53t)
537
538
30
26
5~9
4~5
540
541
:57
13
13
B
5
5
10
~)43
544
545
546
547
548
549
550
551
552
553
5~3·1
555
39
54
32
:~2
51
40
38
38
46
38
27
40
45
44
36
:2
1
3
0
:2
0
1
0
2
1
0
0,
1 I
1 I
01
1
,0
21
1
1
12
10
13
17
15
. 9
10
B
13
8
~)
()
0
~
I
'I
1
1
1
0
0
0
0
()
1
0
1
0
()
0
0
12
2
?
0
0
9
i
0
0
0
0
0
0
"-,
10
'7
~)42
2
1
4
~;:6
{'3
0
0
.-,
11
8
5
'
:1
'9
s-'"
40
21
34
:I
0
",.
o
Table (3-1) continue
DAY
556
557
558
559
5t,O
5/d
562
563
564 .
ACC
- 48
55
21
52
40
~1
SUi
34
46
28
19
38
34
43
44
38
30
27
24
45
37
42
35
37
29
55
42
SEl2.
5fJ3
SD4
40
33
SfJS
31
5f16
587
:~O
56~
566
567
Se)8
569
570
571
572
573
574
57~)
576
577
Sin
579
580
588
589
590
591
592
593
594
595
~96
597
598
599
600
.sOi
602
603
604
605
606
607
608
609
(dO
611
FTL
IN.!
B
18
2
11
8
5
5
17
4
5
14
6
4
11
8
6
11
7
6
7
6
12
14
B
13
10
~)
2~>
46
28
39
47
32
31
37
28
33
29
46
23
26
39
37
27
30
49
36
41
41
26
36
34
25
9
10
10
7
8
10
16
10
18
1 -,
12
6
10
9
11
8
5
11
9,
10
8
13
13
12
11
8
11
12
13
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
1
1
1
7
1
2
2
0
0
1
0
0
0
0
0
1
3
00
1
1
2
0
3
0
1
2
1
4
0
5
2
1
.2
0
1
1
0
0
1
DAY
612
613
614
{dS
616
617
618
619
620
621
6"44
623
624
625
626
627
62El
629
630
{)31
632
633
634
635
63.!,
637
638
639
640
i)41
b42
643
644
645
646
647
648
649 _
650
1.,51
652
653
654
655
656
657
65B
659
660
661
UJ2
663
664
665
666
6tJ7
ACC
24
33
22
22
30
33
31
35
21
14
14
22
25
37
19
17
31
28
35
44
35
28
25
51
39
45
31
28
19
25
35
39
34
FTL
IN~J
10
16
7
7
12
12
12
14
4
11
5
13
6
12
5
6
9
12
8
7
7
17
9
... ·,··1 fJ
15
13
2
9
6
8
6
12
5
28
38
26
29
11
28
32
23
15
8
11
7
14
38
41
37
36
29
30
12
14
12
17
3
9
10
4
7
13
39
19
31
37
14
37
28
40
38
36
12
2
10
6
21
12
11
Aeo
INJ
_FTL
668
669
670
671
672
673.
674
675_
27
21
46
38
28
31
6
2
676
36
677
678
679
680
681
682
683
6B4
685
21·
19
32
33
29
25
21
3:1
19
68b
687
68B
689
22
14
19
0
2
3
1
0
2
1
0
0
4
0
3
1
0
1
1
1
0
1
0
0
1
--0
0
2
2
2
0
3
0
0
1
DAY
2
3
_1
0
3
0
1
0
-0
8
1
2
0
1
0
2
1
2
10
1
1
2
0
3
1
2
0
0
0
2
0
0
0
0
2
1
1
0
3
1
0
4
4
3
2
2
1
0
1
2
0
5
0
0
:2
0
690
691
29
22
~9
21·
17
692
693
6'14
695
696
697
69B
699
700
701
702
703
704
19
26
16
25
36
31
70S
40
40
34
25
706
707
708
21
37
24
20
40
25
13
12
9
7
12
12
5
10
7
3
14
11
11
9
10
~')
7
14
7
6
4
6
5_
3
12
4
8
5
10
2
10
6
t,
'I
11
6
12
12
9
5
2
0
1
0
3
0
0
0
1
...
-I'>
42
Table (3-2)
Basic Statistics of the daily accidents, injuries and
Riyadh Region.
Sum
Mean
Variance
Standard Deviation
Minimum Value
Maximum Value
Correlation Matrix
ACC
INJ
FTL
ACC
INJ
22071
31.17
87.65
9.36
10.00
67
6219
8.78
12.8
3.58
1.00
23
1.00
0.49
0.01
1.00
0.22
for
fatli~es
FTL
660
0.93
1. 70
1. 31
0.00
10
1.00
43
Table ()-))
he quency of the daily accidentB of' R1.yadh area
1982-198)
~or
.. ,.
a..
15
"15",:20
20-25
25-30
30-35
35-40
40-45
••
107
.. S
131
'"
67
18.5
18.6
•.3
"
frequency
•••
PftftrI\q1!'
a...s Mld point
6.2
iD.2
2.~
".. ....
12.5
27.&
32.&
" ..
>"
45-60
23
'6
0.2
47.& •
42.5
~
3.2
52.5
Fnqumey
16.
14.
.
120
/
,
8.
/
60
••
2.
1
L
1U
V
v
..... t---
\
V
~
1U
22.6
2U
8U
.7.&
60
50
"
i:
"0
'0
"
0
0
c:
I:
II
' ill
I
20
100
f'...
t---
Daily accidents in Riyadh area
"·u'"
"'-
200
day number
....
J
44
Table(J-4) : Prequency ot the dally injuries ot Riyadh area for
a.a
-.
......."""
.-.
.-,
1-10
34
• 60
200
1982-1983
....
...
•••
OauMid.
fI(Iint
•••
10- 13
•••
%9.1
26,1
•••
11.5
13-16
••
•••
..."
14.5
17.5
FrtquftlCJ'
220
200
•••
I.'
".
120 •
to •
••
.
••
20
•••
...
11.5
"
..
1'J.5
~20.5
Daily iniuries in Riyadh area
25
20
'"
1:
.5
CD
.;2.
-
.!:
0
ci
"
10
: '. t
I,
I
5
0+---,----.---.---.---.----.---.---.
600 700 800
day number
~
16 -1'
..
~20.5
•
•••
45
~able()-5:
Frequency of the daily fatalities of R1yadh
tor 1982-1983
. area
..
346
Fnqumt')'
".
.,.
48.9
19.
....
\
soo
...
.10
1\
21.
...
...
180
\
~
90
••
a.
o
1
"" ~
•
•
r
>
1
Fwlity
3
Daily fatalities in Riyadh area
10
.9
8
III
6
.!!!
C
"'E
5
0
0
I:
3
2
I
i
!
1
.
•
•
Frequency
13.&
3
>•
26
S.•
..,
46
Table ()-6)
Monthly accidents ,injuries ,and fataiities of Saudi. Arabia for 1974-1985
i'CC
'.
,,-:.
t:·
•• i
0BEJO
IN.j
054~
FTL
()~:}72
Ob 7
(-)77
ODD4
()f:.3~
06~:)
O{?~:
07B
Ot..50 09;
i :? ..?
094
oi.',(' (,
07~:}3
.r.
~.,
\') (
r)"~
~:.";)
O~24
1i
i 443 i 034
'i 062
i ~59B
4 i 202
1 ~:)7
i~53
"j'"iB"!
i~:)j-?
4214
i 26(,
~2
104
O'.?O
,..:-.":-
i
?4
"j "j ::.:: '~.)
() () 'SO 1 T5
i
i
'i 23
O;:~30
",40
() ') :7):J 1 c) '::.
'j
3B
()~:;7
61
():~
63
.~)4
,:...,'..
() i
:>0
60
1200
0770 i :3 i
0[:04 i 4'i
6 1::;
6{}
67
68
70
7'j
.......
OS)::? 'i
10'1
i 6'';/
()9~:;4
147
Ti'
70
79
'I O~)3
2;~
':-::1
i 04~)
401 i ()4'j
49::> 'IO'j 1
2::;;3 i "j 4"7
194
BO
:3 i
7':::
...}
~,'
"X L.
...." J
i
i
i
i
',90
1nS
17?
-,
...... c) {
,.).'
1 :~O
0:339 140
0,-::,·93 ',0ff
4 -;:' L "1
0SJ'i '7 it:.3
i 3~;
i 4(:,i.' OE:O? i :.33
..;t "zrl"-:'
'.l ,:_ .:..
-z ':::'
'.~
f
41
42
43
44
t
,~
'.. ) .':..
'i ::;:;:;5 OE:fj5 1 ;~3
i 2;{i~5
i 042 i (,;tD
,; '71:::
!
-1 :5 7' ~:;
205
197
i ~;.:
::?2i
i ~>l
i :;2::::: 205
i 4(13
.)
:;~6
l.
'
.~)';3
..
i 4 El ~:.)
i 6~)9'
?
"i ~:) '?E; ..::0 i i
i 'j ;.~\
i b:':;;
'1·3 i :.~
~ ;!. ..? {?
'10B9 .j ;~:3
.j F:: . ::}
'I ~6:.4
'I 1.}'? /:'I (}6
1433 'I ~7(;.
1~?j)2
;~O'1
'I ~5>f.
.\ 702 i 391 242
~.'-\
r) !
c· J
82
83
/, C::C)-"
t
_, ••'
I
97
(?9
100
'1 () 1
102
i 03
'104
i 0~;
i 06
1 O'.?
i i 0
i 11
1i 2
i 13
i14
i i 5
i i 6
i i "7
i Hl
11?
'j ?O
1 :~! i
'122
i 2:';)
1 24
'I 2~:;
!
'1 t.
1 ..:.. •.. 1
'.~
I
1 (.) ':1'0
1 6~>O
17E:3
'1580
i :} 1 '1 '1243 i "?"l
'1432 ';1941:}'"?
'14:::;6 .; ''j B3 i .:::.::;
i 2 ":'~ () 1 7 ~':.;
HU FTL
1 -rOB
i '? i 9
1 !3 1 "/ "1481
'17'8a i ;~62
:,! 1 1 3 i ~:520
i 73'/ i ~7 i
i bc)? 'I 4~)O
~ 7~:}'
i 2'7
130
i :3 j
132
1:>3
i 37
22B
23(?
..... I
1788
2147 '1786
'IB26
i '7133 3\ 1
i D\-::'.7
i '.?:30 26t')
:j?~2
i 69:3
iC9B
22DfJ 'i 6"?7
2'i htl 'i ~:) 'J 4
2217 ,,;',67
i 7'14
i
2~;
,.., I::: /1
':•.• J"Y
'j c)46
rjl:::")
,:..
::.'40'1 1796 .........
i 754
:~O
'i 2
21 <j)'l i %4 :.'4~;
2241
2246 i '7 .56 2~)3
1 :34
'i 35
iU,
~,:.·t?
204
i (??
'-,00
<"
i 6D i
i E:':;'.;:·:·
1869
i 90n i 737
17D{) i ~529
'207
i D3;? i4<.?2
1 B60 1~:)3
~.)01:'
'I7B4 ···:oo/!
.':...' "';
i ~56 7 267
24B4
r)DD
.:..
{tCC
M
----_._----
i406
1499 1 3(:}~
i ~:)23
1404 i i 46
1389 1230
i 47()
1443 "j 37'1
'i 5(;)[: i 39';
i :526
i434
i 4(;)7
14·40
.1 .S i :'S
! •• 1
....... 0;0 ..
"',0
,:......,
'~:OD
?iO
i "?::::
"! B ~:
I
"I ~39
102
0797 ') i :5
(-)~?ni
114
107
i 4:3
1 'I 7
i ::;2
"148
2(-)D
"iF3D
','
~>?
i 0'1"2 ()nB~
·104l.:.. () [: ~: i
i 21 'i
i ?:~. i)
:.~
~: i
..
OE:::;4 110
()660
19
-_._----
O.:";9?
:j 'j
'16
i 7'
M
1 Si33
;21'5,
.,,:.r'::'·i"i!
..../ ,:" ..
'
'
}
1972 2"/2
i 'f! 1';' 2.,;1-:3
1 6?7 :~"4(i
1f:333 r j ..;
i S(34
~:,
..: .. ' .• 1
i 3S-'
i 687
'140
'i -4 i
27'14
?64H 1964
I
",'';;' ;)
~:.
,.! ..,
... /·..." •• 1
~,.
"i .\
, .. ' .....
!
47
Table 0-7)
Monthly accidents, injuries and fatalities of
M
i
2
3
4
5
t.;
7
ACC
0::503 OB(') 09
042~;:"1
56 03
()5 1'jb i 7B O~·)
()::;80 20S) :~3
:0,36t:) i i ~:)
:~3
O~421
or;:;) OD
04 i 0 i ~4
25
(')~7n"j
32 23
t)~5'10
147 -12
~
ti.~:9
~T-O
INJ FTL
()52~
~32
M
ACC
49
region for (1974-1985)
R~dh
INJ FTL
M
ACC
INJ FTL
0730 233 34
97
()"{';l9
375 32
50
5i
-> .:..
0784 249 "' S)
0773 278 3~5
(jt)~:
i ~:70
,;:: 1
9f::
0882 4-12 24
100
53
070-? ;"502
~) 7 :.~ :.~
:-3 2 ::.)
0<.:,74 ;"5i i
064~j
316
()918 2(;>0 24
O{?79 333 20
(:,\"??B :.3~>;'?
42
07'25 3 i 2 26
!::"rj
54
09
35
3 ;3
i (-) i
10::!
20
! 0:5
:32
(:7'BS
(,)657 270 27
104
10:i
06i 6 ~$07
0769 ;5:51
i f)6
i (.) 7
0807 292 24
07B3
2'i
11
050\)1'"i62
i7
12
-17
108
'I~·:
'1 ()9
i5
i 6
i 7
0:35014:3
04?4 l~=;i
0511 i7B
(j4~}6
i 99
0:5:94 21:.0
O~:;8{?
24B
18
0716 317 37
'19
O·!)63 306 24
Ol; i ~5 303 33
()636 2"1 3 ~54
1~:)
14
:~0
21
i2
i.4
26
i 6
05:'}6 253 23
Ol)9 r/ 2D:;~
,:~O
(,)706 2",~'M?
:30
23
7i
7:,~
73
74
7:5
76
7"7
30
0662 3'1 '/
35
39
40
41
4')
43
44
04?:::; 276 17
05 i 0 :?B2 24
()S4D 32-;.' 23
(.Is:;:"'," 313 2),4
0624 ;'3,3 i;?
0 ~:5)
7 ~}J 'j [:
264 32
0640 :309 3,5
0653 3~,:i
:50
~.
05:4~;
7El
G764 ;,34 ::!8
0,33:'> 3:.28- 31
(Jij4B 47~5-·E:
0740 402 :,~;
B3
8·4
0790
0726
31'7 :?9
244 33
(:)62D 26~5
i 5
(')7i:~
iG4 '1'1
07 49 :~;6
i :~
B~}
0704 3i -;; 23
B (:i
1"7
..' I
(.) i:.':,
IlU
30:,3
0::;94
:·~;O(-)
32.
D9
076:-3 ;3 i i
()924
07 'i i
:.<;·~O
4'('
::;'7
90
0751
{)(}B:~
0~),4
3B
:;,~)
79
80
Bi
3';
0747 2(,(·) 24
:?99
O~}B6
7{j
31
"1--:,
.....',:..
2:>
2~:;
t.':- {:.\
9i
:39~)
2~>
:~;9)
.-:tt!.:.
3'i 9
-,'" C'''7
...! \.} I
~5i
~.4
34
..:-
1:,.-
,::- •.E
2 :.3i
?3
O,,{,'j 0 ~7'!
7/~·
0"," 15 2:?;D ;'39
'74
D!:~'
i
•• ,'
i1B
1i 9
i 20
i ~, 1
.j 22
'\ :,~3
'I 24
i
OMl1
~BO
:~i
0"(-'""(' i
3BB
~4
i 26
27D 27
3~}
,07~:)5
0035
'f
4~?:
~
...
,-' I
31
337 3~.
31"7 41
0748 3'j6
OBt~3
292
OE::02 34~)
Of:;)'-~
i 3~5:;
'I :,~ i i 44;':':
i i 20 42:
3'-j
27
38
3,4
2~S
H
3~
)
40
33'1 23
300 25
OS<~;2
:~48
(~1?92
097~5
1221 396 18
i (j"'?4 3t!.(;, 2[::
ODe-:-; 3~5B
4~3
OiJG4 4:?7 4:5
091~5
40:-:1 40
O-':~,)
394 33
320 36
08~54
'142
....
I
(')?08 300
129
i::;O
i ::; 1
-\38
139
'140
I \ ..'
I
..;I ,:_
rH'
'H}
i 3:>
'i 3ll
137
'") L.
")";' f,
AM
0816 29=; 34
30:;: 37
-""} 7 'H) Ml·.,
Oi)3/.:, ":M
(')B92 306 :~o
;~7
141
:5;?9 i '?
() t., ;.:~ 1 3';'"17 3~:)
(){,(-)9
24
'125
'i 26
i~}
0644
9:~
i i 0
i 1i
1 L~
1 1 :3
'11 A
i i ::>
i i ,~\
-\ 1 ('
;.:~9('S
0878 :352
:~s5
0998
~:'9
~)30
'ii6f.:.44147
i096 340 :.26
38(J :35
:3::>B 45:
1 'i 99
I; 092
i "1(:;0
.) OD 'j
410 34·
2{1' '\ 22
48
Table ()-8)
Monthly aCCidents.injuries,and fatalities of Makkah region for" 1974-1985
-------
M
2
3
nu
ACC
FTL
154 0i (ia O;~2
144 0196 020
1·42 0, D9 0:~5
i~57 , .
02"1:4 (·)'i9
,'\CC
"19
50
5i
0297
333 0392
M
(·)~"58
ACC
97
45~)
Ob 17 1'05
3B1
99
397 (:)571
42"1 04~:)3
046<) 07f,
077
100
-'
6
9:3 029
1;.68 (~i
1'13 0270 042
400 0432 065
'1 tii
7
20B 02D3 02B
!8
1 98 0279 039
-\ 9~:
047
199
027
2i7 0307
3 i i 0365 079
334 03B6
374 046B
on
39~:) 0~)(-O
0[36
4
.
.." .
1 ,.)
17;
",,'l
•• F .:••
58
0233 042
0;,:,)0 04{)
3i3 027i Oe,8
(-)2.::':.
192
03:~7
0~.'9
")7 My
25
,.., .-
.::'C)
28
29
30
"j,-?
0330
270 0372 053
02~5
2-j 9
72
044
292 0324 048
288 030"7 019
270 0318 043
0:;~i
058
363 04~;
062
36
8:;
40
070
(-)~?DO
046
0304 073
339 03~;-4
0'50
41
~30(1
42
:;B2 02·"{'·1 0·44
3()6 (J3'1 f.? (·)46
213 0260 0:;0
B4
03~)O
43
A·4
0222 04·1
~
'1 (-)D
340
()4~}9
OEl4
01.S7
109
i i0
442 Ob22 052
29') 039'i
4~j
O"49~:)
O,ss:'
333 0419 06i
1i 1
465
460
46"\
600
0~:;'t.
072
096
3i6 0410
06~:)
~;0B
O~:;.-)
04:~B
(-)-;-'3
0~52·i
0~)7
04i:3 041
363 0453 OBO
[i(.)
470 06fl8 0'11
452 06B8 1 ', -z
52·(' 0693 "; 31
i 2t)
341
T?
78
79
437 ()657 087
469 06~>
i 49
0~->1"7
346 0423
2c";.::: 02:A"l O~}6
25(. 0:';;3c) (.):;()
406 Co4';"? OB7
42~:)
442 0621 070
49::} 0613 1 .! '1'
400 V'\O,) 072
402 0'526 (J";5
419 ()~:;46
i :' 1
0307 054
B1
B2
03
:~5
1 ()7
::373
3'1 '7' 0420 G'=?9
:~5(')
040c) O··lB
473 o~: {? ~:}
.j OD
41 i (·)4D~:
'.J
34
372 043D 089
075
:;82 0561 0f,1
432 0472 070
,02
31:; 0444 070
3:;9 0473 092
03(1 "? 046
2(:· 7 O~:2
i00
-:.. '-) '.~
07~)
103
104
105
'106
0:H~
209 O:;':::?2 040
23
24
044:5 069
~,60
HU FTL
{is
374 0444 0b6
4DD 0474 072
'0
'~I
INJ FTL
36"," 0478 064
3B3 0497 064
3~;
04~57
0l:'-7
04(37 076
~6)
418 05(.:)7 099
403 0428 072
431 04B1 ODO.
443 0~)35
(·)79
34B 0526 "120
381 046'7 06'?
O,~4:'-;
i i3
i i 4
i 'j ~:)
'1,6
i 17
j i El
119
i ~'O
i :~ 'I
i ;22
12:3
i 24
i :2 ~:)
126
i ~. 7
480 O:"}3t. 049
128
513 0635 061
12'1
·~i
1:30
131
i ~:'2
133
134
(·)~;93
08~:;
V~)7
4~:;
Ol:..2
06c)2 100
0 Q ')
6~5
OB42 1 2'1
:;2~S
133
56\ 0737 096
{;3D iO~)"7
i6::?
47B ()(-}37 f)84
:"}?b 073i
O~;B(.
Ot:;'2
0404
4f, 1 0:;12
43') 0'526
4f:,() 060D
074
074
(18B
070
8 0792 ·10B
061:.·)9 i 02
431 064.0 0'13
~)20
636 OnD9 152
3a'; 0471 062
B6
3l)4 0460 06:.3
B8
B9
90
343 O,,·1- 7? O\~:,{?
3Di 0480 04:")
(·)2B5 O·l~5
351
(Y53
364
-.. -,. Ci, 047
i38
91
370 0471 066
()452 066
313 04i2 () f:.. 9
1.39
92
93
30i
427 050B (~7D
440 (-)599 084
332 04~}6
102
542 0b71 073
~)32
069b ""j 02
140
0553 050
420 0623 i 0"1
37::> 0539 084
3S'4 0~593
083
463 0742 093
2·1 9 0:.~63
062
i f(4 o2 B··'" 0·?8
'I (.7'S {:)237 O~)i
9~)
273 (·)4(,")0 099
9f,
'14
"
t:J ,~).;:
'I
3~5
iU,
41
142
'j 43
-j
144
38'"; OS97 06·,
":'(J,~
049, 075
39:~
(~u,{"06
046
49
,.
Table (3-9)
Basic Statistics of the Monthly Accidents. Injuries and Fatalities
in Saudi Arabia
Sum
Mean
Variance
Standard deviation
Minimum value
Maximum value
ACC
INJ
FTL
231008
1604.2
210362
458.7
190636
1323·9
16709
408.8
753
2714
545
2442
29629
205.8
4578.6
67.7
65
392
1.0
0.897
0.732
1.0
0.884
1.0
Correlation Matrix
ACe
INJ
FTL
50
Table(3-10): Basic statistics of the monthly accidents, injuries
and fatalities of the Riyadh region.
Sum
IOean
Variance
accidents
injuries
fatalities
105724
734.2
43299
300.7
5321
4008
27.8
107.3
72.9
80
10.4
Standard deviation
31395
177.2
Minimum value
Maximum value
358
1221
Correlation matrix:
Accidents
1.0
Injuries
Fatalities
475
0.669
1.0
0.377
0.525
3
74
1.0
Table(3-11): Basic statistics of the monthly accidents, injuries
and fatalities of the Makkah region.
Sum
Mean
Variance
Standard deviation
Minimum value
lI:aximurn value
accidents
injuries
fatalities
5280)
)66.7
1240)
111.4
66741
46).5
24818
10154
70.5
764.8
27.7
656
157.5
1B9
1057
Accidents
Injuries
1.0
0.91
1.0
Fatalities
0.706
0.78
142
19
162
Correlation matrix:
1.0
51
..Table(3-12):
Year
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
Total
Yl
Y2
Y3
04147 04583 0570
07197 06530 0834
09808 07901 1058
10897 08771 1154
13475 10532 1594
15709 11606 1975
15785 11413 2033
18051 14824 2378
17743 16832 2871
18758 16218 2731
17897 15872 2427
21597 18616 2953
24594 21475 3199
27348 21850 3038
29052 22630 3276
252058 209653 32091
Xl
6436283
6622937
6815004
7012642
7216010
7439703
7662894
7892780
8129560
8373444
8742549
9022312
9311016
9608970
9916454
Saudi Arabia
X2
0144768
0180185
0242974
0355022
0514361
0774443
1112973
1432909
1723116
2069479
2467903
3018811
3569009
3919871
4144245
. -
X3
X4
X5
031542 010324 009689
033357 020271 012335
047209 032639 022890
057901 050279 047574
098758 084347 065039
117911 136571 103888
173788 182226 133717
257176 164482 136447
241153 115679 159272
206549 142423 197029
150178 175123 215776
198921 238164 307905
240031 261478 284952
283033 157283 184556
340333 099001 120997
2477840 1870290 2002066
X6
02249
01843
05951
11833
08514
16515
19244
16074
12779
01020
00000
00000
00000
01376
02348
99746
X7
0543
0968
1309
2362
1439
3108
3343
2933
2477
4413
4164
2551
2584
3719
1868
37781
Table(3-13): Riyadh region
Year
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
Total
Yl
01524
03425
05469
05694
07266
08167
08698
08327
07275
08513
07905
09868
10206
11932
11873
116142
Y2
1051
1562
2080
1771
3051
3660
3454
3498
3297
4268
3917
4096
3644
4553
4090
47992
Y3
082
127
152
175
301
301
444
324
285
380
299
337
375
389
398
4369
Xl
1167708
1201572
1236418
1272275
1309171
1349754
1390247
1431954
1474913
1519159
1586124
1636881
1689259
1743316
1799101
X2
0067607
0079525
0105144
0139244
0189343
0270691
0415282
0494927
0575080
0655495
0773795
0985378
1160663
1270110
1297007
X3
X4
010588 04330
007788 06869
023417 13141
015703 13451
023620 25798
038471 40892
059317 80663
063548 36508
055299 31427
032952 27315
017826 45000
044655 79000
075151 78550
0832A5 46890
130063 10483
681643 540317
X5
005084
004191
008795
015835
021956
033135
054700
037140
043863
051850
071000
130074
094635
056107
016039
644404
X6
X7
1019 0218
0724 0134
3349 0334
4519 0295
1863 0482
5860 1461
8166 1062
4955 1042
4263 0600
0600 0650
0000 1300
0000 1916
0000 1800
0000 3000
0000 0375
35318 14669
52
Table(3-14): Makkah region
Year
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
Total
Y1
1270
1556
2017
2284
2860
3824
3421
4407
4486
4561
4748
5426
6320
5953
4513
57646
Y2
Y3
1781 0235
1891 0326
2521 0431
3084 0403
3676 0541
4364 0728
3637 0710
5237 0902
5924 0938
5665 0899
5837 0860
7033 1122
8420 1148
7514 1047
6350 0856
72934 11146
Xl
1609940
1656629
1704672
1754108
1804977
1860931
1916758
1974261
2033488
2094492
2186818
2256797
2329012
2403540
2480453
X2
0031936
0045939
0066022
0108968
0161389
0255636
0355744
0493655
0599548
0738022
0864489
1039250
1194933
1312440
1400080
X3
X4
10400 02323
10891 08114
10153 09636
18490 18498
24643 26741
28138 47042
60162 45806
60229 78729
53568 38671
48778 55564
55181 49523
51617 67342
48425 67230
61359 48226
57434 33172
599468 596617
X5
001989
004783
008575
019393
021609
040359
046394
051872
061689
078965
. 074160
105617
088320
068449
053441
725615
X6
0533
0447
1162
3483
3638
6274
6776
6576
4865
0036
0000
0000
0000
0568
0169
34527
X7
0186
0659
0710
1572
0433
0572
1132
0734
0668
3083
2005
0369
0089
0186
0846
13244
Table(3-15): Dammam region
Year
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
Total
Yl
0455
0872
0841
1184
1368
1386
1292
1985
1805
1156
0976
1130
1183
1419
2396
19448
Y2
0562
1127
1091
1453
1650
1085
1506
2187
2379
1501
1147
1604
1741
1987
2967
23987
Y3
097
181
179
218
324
312
307
340
449
423
381
309
365
395
533
4813
Xl
0764213
0786376
0809181
0832648
0856795
0883355
0909855
0937151
0965265
0994223
1038049
1071266
1105546
1140923
1177432
X2
023482
029044
038243
051868
074141
113356
144234
199784
259362
344350
419719
505941
608346
656917
697984
X3
06091
08671
07438
10092
31212
28147
22539
68027
70097
60145
38118
60115
63568
77785
78746
630791
X4
X5
X6
01857 0341
01428
02489
02577 0360
03887
04178 0890
04846
07195 1361
08775
11710 1379
16545 2110
19687
15076
12958 2045
25350
26750 2750
32175 2048
24414
44210 0086
39777
35498
37729 0000
38600 0000
47350
56200 0000
45155
18936
28950 0300
14003
24760 1801
306671 ·346394 15471
X7
071
136
244
223
409
873
799
700
941
544
674
136
554
385
503
7192
53
Table(3-16): North region
Year
Yl
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
Total
0527
0747
0722
0973
0979
1103
1222
1453
1509
1851
1791
2165
2831
2889
3467
24229
Y2
0683
1093
0975
1239
1013
1094
1452
1918
1919
1611
1924
2116
3381
2999
3432
26849
Y3
Xl
093
113
154
166
228
281
253
349
399
425
405
443
555
480
545
4889
0957919
0985699
1014285
1043700
1073967
1107260
1140477
1174692
1209932
1246229
1301164
1342801
1385769
1430114
1475877
X2
016068
018651
022371
032984
048721
068651
089582
111397
132889
154811
193388
217332
247164
271426
293905
X3
02987
04069
04239
07134
07277
07666
06820
37043
33345
40501
21378
18477
21822
23172
23198
259128
X4
01664
01645
02468
06206
09967
11184
13438
10757
08544
08868
20240
14139
17824
13917
13438
154299
X5
X6
00572 "0230
00655 0246
00921 0313
03254 0884
04925 0740
07512 1124
07134 0243
09975 0748
11904 0847
12530 0242
18260 0000
09732 0000
11975 0000
09984 0281
08775 0201
118108 6099
X7
066
037
018
269
105
110
116
335"
197
102
058
047
031
042
037
1570
Table(3-17): Qaseem region
Year
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
Total
Yl
0167
0318
0379
0437
0478
0582
0410
0456
0681
0884
0804
1060
1184
1646
1284
10770
Y2
0208
0487
0691
0738
0453
0627
0462
0638
0934
0973
1207
1457
1783
2174
1801
14633
Y3
033
055
064
126
097
180
134
158
253
205
207
330
345
364
297
2848
Xl
X2
529181
544528
560319
576569
593289
611681
630031
648932
668400
688452
718799
741801
765537
790035
815316
003880
004987
008701
017624
031201
048566
080785
095192
110539
121080
139501
168335
218275
237615
257286
X3
00708
01184
01383
02693
05658
07065
10439
14833
11098
10283
05983
09589
14423
15422
10179
120940
X4
00429
01010
03351
07271
09877
12827
21946
09217
09490
05974
12290
17902
32153
12644
13689
170070
X5
00140
00084
00283
01315
03199
03832
08703
04688
05315
04502
06000
10859
17699
06560
05928
79107
X6
X7
041
013
079
337
500
700
1543
465
509
034
000
000
000
055
017
4293
00
00
01
00
01
06
27
37
33
00
95
61
77
45
35
418
54
Table (3-18): South region
Year
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
Total
Yl
0204
0279
0380
0325
0524
0647
0742
1423
1987
1793
1673
1948
2870
3509
5519
23823
Y2
0298
0370
0543
0486
0689
0776
0902
1346
2379
2200
1840
2310
2506
2623
3990
23258
Table\3-19):
Y3
030
032
078
066
103
173
185
305
547
399
275
412
411
363
647
4026
ComparIng aClents~
of ten years
1
ACe
~aUdi
Arabia
fH1vadh reJ!lon
regIon
",ak~h
juammam regIon
region
~orth
J'e~lOT
~seru
region
Sout"'l
. Xl
1340318
1379188
1419185
1460342
1502692
1549275
1595753
1643625
1692933
1743721
1820585
1878844
1938965
2001012
2065044
Yt:l08
!:>4b9
201-"
b41
722
3 -{\,I
380
X5
00047
00045
00138
00582
01640
02505
03828
06022
04326
04972
08627
13023
16123
14506
12054
88438
X6
085
053
158
249
394
447
471
580
247
022
000
000
000
172
160
3038
X7
002
002
002
003
009
086
207
085
038
034
032
022
033
061
072
688
injuries and fatalities
ArabIa.
in a
period
X2
001795
002039
002493
004334
010566
017543
027346
037954
045698
055721
077011
102575
139628
171363
197983
in Saudi
X3
00768
00754
00579
03789
06348
08424
14511
13496
17746
13890
11692
14468
16642
22050
40713
185870
Y 7 3
INJ
1 9 8
FTL
-19UI
10t>8
201:10
152
431
179
154
64
78
2.521
1091
97!:>
691
543
X4
00150
00144
00156
01007
04189
03939
05297
03921
03133
04925
12572
12431
20566
16670
14216
103316
increasln,::
;3
ACC
I NJ
24594
10206
6320
1183
2831
1184
2870
21475
3644
8420
1741
3381'
1783
2506
FTL
3199
375
1148
365
555
345
411
ACC
151
87
213
41
292
212
655
"
I NJ
FTL
172
75
202
147
166
104
260
439
234
60
247
158
362
427
Table (3-20)
Basic statistics of the Yearly datll of Slludi Arabia
Yl
Y2
13
Xl
252058
209653
32091
120202560
25670072
2477840
139'76.9
2139.4
8013504
1711338
5756.2
908.4
1118183
1419210.6
X2
X5
X6
X7
1870290
2002066
99746
37781
165189·3
124686.0
133471. 1
6649·1
2518·5
98148.3
76019·0
93652
6899
1143·8
1.0000
0.0740
1.0000
X3
X4
SUM::
MEAN
16804.1
STANDARD DEVIATION
7081
CORRELATION MATRIX
2
3
4
5
6
7
8
9
10
1.0000
0·9818
0·9541
0·9720
0·9486
0·9315
0.710
O. "'1~;
- o. ::'lGFJ
0·5535
1 .0000
1 .0000
0·9767
0.9820
1.000
0.9430
0.9090
0.991
0·9657
0.9355
0.894
0·9295
0.713
0.7332
0.7942
0.8086
0.8512
0.798
- 0.2929 - 0.1694 - 0·385
0.6245
0·5479
0·543
1.0000
0.8702
0.6774
0·7761
- 0.463
0.4730
1.0000
0.6401
0.6637
- 0.067
0.510
1. 0000
0.9377
- 0.053
0.6659
1.0000
- 0·3050
0.6515
'"
.
56
TableI3-21': Basic statistics 01 the yearly data of Rlyadh region.
VI
116142
7743
2858
SUI
lean
s.d •
.' Correlation
Y1
Y2
Y3
Xl
X2
13
14
IS
16 .
17
aatrh
1.0000
0.9233
0.9071
0.9061
0.8695
0.8119
0.5762
0.5764
- 0.1474
0.6776
Y2
V3
11
12
13
I4
47992
3199
1078
4369
291
109
21807852
1453857
202867
8479291
565286
442986
681643
45443
33312
540317
36021
26203
1.0000
0.9104
1.0000
0.7746
0.8544
1.0000
0.7992
0.7270
0.9903
0.7128
0.7928
0.6354
0.6804 . 0.4884
0.5943
0.6476
0.5778
0.6295
- 0.1642 - 0.0464 - 0.4536
0.6848
0.5733
0.6424
1.0000
0.7961
1.0000
0.4870
1.0000
0.2856
0.8737
0.6280
0.2259
- 0.5025 - 0.0933 - 0.1235
0.6636
0.7137
0.3822
IS
844404
42960
35429
16
17
35318
2355
2641
14669
978
803
1.0000
1.0000
0.2470
0.7059 - 0.1862
1.0000
·.TableI3-22': Basic statistics of the yearly data of Haklcah region.
SUI
lean
s.d.
Y1
Y2
Y3
11
12
13
14
IS
16
17
57646
3843
1567
72934
4862
2063
11146
743
292
30066876
2004458
279697
8668051
577870
486541
599468
39965
20225
596617
39775
23172
725615
48374
32017
34527
2302
2676
13244
823
800
1.0000
0.8087
0.8107
0.0910
0.1561
1.0000
0.8552
1.0000
0.1500 - 0.2095
1.0000
0.1060
0.1690 - 0.0821
Correlation
Y1
V2
Y3
11
X2
13
I4
IS
16
X7
.. trix
1.0000
0.9867
0.9846
0.9094
0.8898
0.8420
0.8530
0.933i
- 0.1570
- 0.0001
1.0000
0.9657
1.0000
0.8787
i.OOOO
0.9345
0.8540
0.9242
0.9926
0.7991
0.8640
0.8203
0.8860. 0.6541
0.7892
0.9528
0.9160
0.8366
- 0.2351 - 0.0970 - 0.3391
- 0.0380
0.0094
0.0199
1.0000
0.7816
0.6141
0.8203
- 0.4330
- 0.0160
1.0000
TableI3-23): Basic statistics 01 the yearly data 01 Da.... region.
.
YI
Y2
Y3
11
12
X3
14
IS
:16
17
.,
SUB
lean
s.d:
Correlation
Yl
V2
Y3
11
12
13
I4
IS
16
Xl
19U8
1297
481
23987
1599
601
48i3
321
115
14272278
951485
132766
.. trlx
1.0000
0.9315
0.7664
0.5468
0.4504
0.7143
0.1465
0.2790
0.6611 .
0.5457
1.0000
0.6187
0.6798
0.6139
0.8143
0.2345
0.4080
0.4269
0.3835
1.0000
0.8292
1.0000
0.7458
0.9647
0.8770
0.6662
0.6753
0.5420
0.6894
0.7935
0.1923 - 0.1788
0.6168
0.2764
4166771
277785
244064
1.0000
0.8360
0.6400
0.7694
- 0.3008
0.1429
630791
42053
27432
306671
20445
15551
346394
23093
16663
1.0000
1.0000
0.6452
0.9438
1.0000
0.7752
0.0672 - 0.3217 - 0.3081
0.3324
0.3827
0.4034
15471
1031
947
1.0000
0.5734
7192
480
261
1.0000
'
57
Table(3-241: Haslc stallstics of lhe yearly data 01 Norlhl region.
SUII
lean
s.d.
Y1
V2
V3
11
X2
24229
1615
833
26849
1790
877
4889
326
154
17889884
1192659
166420
1919340
127956
96926
Correlalion lalri.
1.0000
Y1
Y2
0.9699
V3
0.9348
Xl
0.9750
0.9776
12
13
0.5518
14
0.6986
IS
0.6099
- 0.4190
16
17
- 0.2747
1.0000
0.9109
1. 0000
0.9700
0.9370
0.9427
0.9575
0.5443
0.7257
0.6854
0.7948
0.5883
0.8086
- 0.3993 - 0.3221 . - 0.1970 - 0.1447 -
1.0000
0.9950
0.6170
0.7970
0.7440
0.4160
0.2380
13
259128
17275
12678
I4
IS
16
11
154299
10287
5585
118108
6099
407
362
1570
105
7874
5073
1.0000
0.5968
1.0000
0.7728
0.4140
1.0000
0.7481
0.8470
0.7200
1.0000
- 0.4720 - 0.0537 - 0.2979 - 0.2176
- 0.2860
0.3230 - 0.1050
0.0540
1.0000
0.6766
93
1.0000
Table(3-251: Basic statislics of the yearly data of Qasee. region.
"
Y1
10770
718
418
Stili
Bean
s.d.
Correlation
VI
V2
V3
Xl
12
13
14
IS
16
17
Y2
i3
11
X2
13
14
IS
16
11
14633
976
585
2848
190
109
9882870
858858
91935
1543567
102904
86802
120940
8083
5022
170070
11338
8212
79107
5274
4S36
4293
418
28
31
1.0000
0.6528
0.7176
0.1432
0.5452
1.0000
0.9510
0.2494 .
0.6669
1.0000
0.0380
1.0000
0.7460 - 0.1969
286
422
.atril
1.0000
0.9754
0.9332
0.9369
0.9394
0.6929
0.5236
0.6148
- 0.3699
0.5821
1.0000
0.9202
1.0000
0.9283
0.9413
1.0000
0.9322
0.9319
0.9907
0.6346
0.7911
0.7707
0.5344
0.6728
0.6280
0.7687
0.7151
0.6272
- 0.4443 - 0.2334 - 0.2600
0.6514
0.6942
0.7273
1.0000
0.7784
0.6303
0.7214
- 0.2702
0.7073
1.0000
Table(3-26I: Basic stallsllcs 01 lhe yearly dala 01 Soulh region.
sua
lean
s.d.
Y1
V2
V3
23823
1588
1478
23258
1551
1092
4026
268
193
11
25031482
1668766
232855
X2
13
14
IS
16
894049
59603
64948
185870
12391
10321
103316
6888
8631
88438
5896
5619
3038
203
191
11
'688
<46
.~
Correlation latr!1
VI
Y2
V3
Xl
X2
13
14
X5
16
17
1.0000
0.9607
0.8752
0.9154
0.9591
0.9513
0.7793
0.8148
- 0.2439
0.1661
1.0000 .
1.0000
0.9599
1.0000
0.9460
0.8703
0.9209
0.7950
0.9547
0.9273
0.8947
0.8731
0.7752
0.6470
0.9105
0.8338
0.7397
0.9439
- 0.3111 - 0.1752 - 0.2796
0.1418
0.2251
0.2096
1.0000
0.8736
1.0000
0.9053
0.6810
1.0000
0.9248
0.7254
0.9692
1.0000
- 0.3381 - 0.0210 - 0.3620 - 0.3375
0.1470
0.1570
0.3992
0.1510
1.0000
0.5788
1.0000
58
Table (3 - 27) : Accident rate per 1000 yehicle.
Year SAA
1971
1972
1973
1974
1975
1976
1977
197B
1979
19BO
19B1
19B2
19B3
19B4
1985
2B.6
39.9
40.4
30.7
26.1
20.3
14.2
12.6
10.3
09.1
07.3
07.2
06.9
07.0
07.0
lean 17.9
RYH
22.5
43.1
52.0
40.9
38.4
30.2
20.9
16.8
12.7
13.0
10.2
10.0
OB.8
09.4
09.2
22.5
Table (3 - 2B)
Year
1971
1912
1973
1974
1975
1976
1977
1978
1979
1980
1981
1962
1963
1984
1985
SM
31.7
36.2
32.5
24.7
20.5
15.0
10.3
10.3
09.6
07.8
06.4
06.2
06.0
05.6
OS.5
mean 15.2
RYH
15.6
19.6
19.8
12.7
16.1
13.5
06.3
07.1
OS.7
06.5
OS.1
04.2
03.1
03.6
03.2
09.6
IIKH
39.B
33.9
30.6
21.0
17.7
15.0
09.6
OB.9
07.5
06.2
05.5
05.2
OS. 3
04.5
03.2
14.3
DAM
19.4
30.0
22.0
22.B
1B.5
12.2
09.0
09.9
07.0
03.4
02.3
02.2
02.0
02.2
03.4
11.1
URT
32.B
40.1
32.3
29.5
20.1
16.1
13.6
13.0
11.4
12.0
09.3
10.0
11.5
01.6
11.8
lB.3
QSH
43.0
63.B
43.6
24.B
15.3
12.0
OS. 1
04.8
06.2
07.3
05.8
06.3
OS.4
06.9
05.0
17.0
SUT
113.7
136.B
152.4
075.0
049.6
036.9
027.1
037.5
043.5
032.2
021.7
019.0
020.6
020.5
027.9
054.3
Injury rate per 1000 yehicles
IIKH
SS.B
41.2
36.2
26.3
22.8
17.1
10.2
10.6
09.9
07.7
06.8
06.8
07.1
05.7
04.5
1B.2
DAH
23.9
38.B
28.5
28.0
22.3
09.6
10.4
10.9
09.2
04.4
02.7
03.2
02.9
03.0
04.3
13.5
HRT
42.5
58.6
43.6
37.6
20.8
16.0
16.2
17.2
14.4
10.4
10.0
09.7
13.7
11. 1
11.7
22.2
QSH
53.6
97.7
79.4
41.9
14.5
12.9
05.7
OB..7
08.5
08.0
06.7
08.7
08.2
09.1
07.0
24.7
SUT
166.0
lB1.5
217.8
112.1
085.2
044.2
033.0
035.5
052.1
039.5
023.9
022.5
018.0
015.3
020.2
069.8
Table (3 -29) : Fatality rate per 1000 vehicles
Year SM
1971
1912
1973
1974
1975
1976
1977
1978
1979
1960
1981
1982
1983
19B4
1985
03.9
04.6
04.4
03.3
03.1
02.6
01.6
01. 7
01.7
01.3
01.0
01.0
00.9
00.8
00.8
lean 02.2
RYH
01.2
01.6
01.5
01.3
01.6
01.1
01.1
00.7
00.5
00.6
00.4
00.3
00.3
00.3
00.3
00.9
HKH
07.4
07.1
06.5
03. 7
03.4
02.9
02.0
01.8
01.6
01.2
01.0
01.1
01.0
00.8
00.6
02.8
DAM
04.1
06.2
04.7
04.2
04.4
02.6
02.1
01.7
01.7
01.2
00.9
00.6
00.6
00.6
00.8
02.4
HRT
05.8
06.1
OB.9
OS. 0
04.7
04.1
02.8
03.1
03.0
02.8
02.1
02.0
02.2
01.8
01.9
03.6
QSM
08.5
11.0
07.4
07.2
03.1
03.7
01.7
01. 7
02.3
01.7
01.5
02.0
01.6
01.5
01.2
03.7
SUT
16.7
15.7
31.3
15.2
09.8
09.9
OB.8
08.0
12.0
07.2
03.6
04.0
02.9
02.1
03.3
09.9
Table (3 - 30)
Year
1971
1912
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
SM
110.5
90.7
80.6
80.5
78.2
73.9
12.3
82.1
04.9
86.5
88.7
86.2
87.3
79.9
17.9
lean 84.7
RYH
67.0
45.6
38.0
31.1
42.0
44.8
39.7
42.0
45.3
50.1
49.6
oiLS
35.7
38.2
34.5
43.1
injury rate per 100 accidents
HJ(!I
DAM
140.2
121.5
125.0
135.0
128.5
114.1
IOB.3
118.8
132.1
124.2
122.9
129.6
133.2
126.2
140.7
126.6
123.5
129.2
129.7
122.7
120.6
78.3
116.6
110.2
131.8
129.8
117.5
142.0
147.2
140.0
123.8
124.2
HRT
129.6
146.3
135.0
127.3
103.5
99.2
118.8
132.0
127.2
87.0
107.4
97.7
119.4
103.8
99.0
115.6
QSft
124.6
153.1
182.3
168.9
94.8
107.7
112.7
139.9
137.2
110.1
ISO. 1
137.5
150.6
132.1
140.3
136.1
SUT
146.1
132.6
142.9
149.5
131.5
119.9
121.6
94.6
119.7
122.7
110.0
118.6
87.3
74.8
72.3
116.3
Table (3 - 31) : Fatality rate per 100 accidents
Year
1971
1972
1973
1974
1975
1976
1917
1978
1979
1980
1981
1982
1983
1984
1985
SM
13.7
11.6
10.8
10.6
11.8
12.6
12.9
13.2
16.2
14.6
13.6
13.7
13.0
11.1
11.3
lean 12.7
RYH
5.4
3.7
2.8
3.1
4.1
3.7
5.1
3.9
3.9
4.5
3.8
3.4
3.7
3.3
3.4
3.9
HKH
18.5
21.0
21.4
17.6
18.9
19.0
20.8
20.5
20.9
19.7
18.1
20.7
18.2
17.6
19.0
19.5
DAM
21.3
20.8
21.3
18~4
23.7
22.5
23.8
17.1
24.9
36.6
39.0
27.3
30.9
27.8
22.2
25.2
HRT
17.6
15.1
21.3
17.1
23.3
25.5
20.7
24.0
26.4
23.0
22.6
20.5
19.6
16.6
15.7
20.6
QSH
19.8
17.3
16.9
28.8
20.3
30.9
32.7
34.6
37.2
23.2
25.7
31.1
29.1
22.1
23.1
26.2
SUT
14.7
11.5
20.5
20.3
19.7
26.7
24.9
21.4
27.5
22.3
16.4
21.1
14.3
10.3
11.7
18.9
59
Table(3-321:Accident rat. per
( X 10000 I
Year SAA RYH HKH DAM
1971 OS.4 13.1 7.9 06.0
1972 10.9 28.5 9.4 11.1
1973 14.4 44.2 11.8 10.4
1974 15.5 44.8 13.0 14.2
1975 18.7 55.5 15.9 16.0
1976 21.1 60.5 20.6 15.7
1977 20.6 62.6 17.8 14.2
1978 22.9 58.2 22.3 21.2
1979 21.8 49.3 22.0 18.7
1980 22.4 56.0 21.8 11.6
1981 20.5 49.8 21.8 09.4
1962 23.9 60.3 24.0 10.6
1983 26.4 60.4 27.0 10.7
1984 28.5 68.4 24.8 12.4
1985 29.3 66.0 18.2 20.4
lean 20.2 51.8 18.6 13.5
Table(3-331: Injury rate
( X 10000 I
Year SAA RYH HKH
1971 07.1 09.0 11.1
1972 09.9 13.0 11.0
1973 11.6 16.8 14.8
1974 12.5 13.9 17.6
1975 14.6 23.3 20.4
1976 15.6 27.1 23.5
1977 14.9 24.9 19.0
1978 18.8 24.4 26.5
1979 20.7 22.4 29.1
1980 19.4 28.1 27.1
1981 18.2 24.7 26.7
1982 20.6 25.0 31.2
1983 23.1 21.6 36.2
1984 22.7 26.1 31.3
1985 22.8 22.7 25.6
lean 16.8 21.5 23.4
unit population
HRT
05.5
07.6
07.1
09.3
09.1
10.0
10.7
12.4
12.5
14.9
13.8
16.1
20.4
20.2
23.5
12.8
QSH
03.2
05.8
OS.8
07.6
08.1
09.5
OS.5
07.0
10.2
12.6
11.2
14.3
15.5
20.8
15.8
10.3
SUT
01.5
02.0
02.7
02.2
03.5
04.2
04.7
08.7
11.7
10.3
09.2
10.4
14.8
17.5
26.7
08.7
per unit pupulation
DAM
07.4
14.3
13.5
17.5
19.3
12.3
16.6
23.3
24.7
15.1
11.1
15.0
15.8
17.4
25.2
16,6
Table(3-341:Fatality rate per
( 1'10000 ).
Year SA! RYH HKH DAM
1971 00.9 00.7 1.5 01.3
1972 01.3 01.1 2.0 02.3
1973 01.6 01.2 2.5 02.2
1974 01.7 01.4 2.3 02.6
1975 02.2 02.3 3.0 03.8
1976 02.7 02.2 3.9 03.5
1977 02.7 03.2 3.7 03.4
1978 03.0 02.3 4.6 03.6
1979 03.5 01.9 4.6 04.7
1980 03.3 02.5 4.3 04.3
1981 02.8 01.9 3.9 03.7
1982 03.3 02.1 5.0 02.9
1983 03.4 02.2 4.9 03.3
1984 03.2 02.2 4.4 03.5
1985 03.3 02.2 3.5 04.5
lean 02.6 02.0 3.6 03.3
HRT
07.1
11.1
09.6
11.9
09.4
09.9
12.7
16.3
15.9
12.9
14.8
15.8
24.4
21.0
23.3
14.4
QSH
03.9
08.9
12.3
12.8
07.6
10.3
07.3
9.80
14.0
14.1
16.8
19.6
23.3
27.5
22.1
14.0
SUT
02.2
02.7
03.8
03.3
04.6
05.0
05.7
08.2
14.1
12.6
10.1
12.3
13.0
13.1
19.3
08.7
unit population
NRT
01.0
01.1
01.5
01.6
02.1
02.5
02.2
03.0
03.3
03.4
03.1
03.3
04.0
03.4
03.7
02.6
QSH
00.6
01.0
01.1
02.2
01.6
02.9
02.1
02.4
03.8
03.0
02.9
04.5
04.5
04.6
03.6
02. 7
SUT
00.2
00.2
00.6
00.5
00.7
01.1
01.2
01.9
03.2
02.3
01.5
02.2
02.1
01.8
03.1
01.5
Table(3-3S): Accident rate per unit
population after IOR transfor.atlon.
Year RYH HKH DAM HRT QSft SUT
1971 1.12 0.90 0.78 0.74 0.51 0.18
1972 1.46 0.97 1.05 0.88 O. 76 0.30
1973 1.65 1.07 1.02 0.85 0.83 0.43
1974 1.65 1.11 1.15 0.97 0.88 0.34
1975 1.74 1.20 1.20 0.96 0.91 0.54
1976 1.78 1.31 1.20 1.00 0.98 0.62
1977 1.80 1.25 1.15 1.03 0.81 0.67
1978 1.77 1.35 1.33 1.09 0.85 0.94
1979 1.69 1.34 1.27 1.10 1.01 1.07
1960 1.75 1.34 1.06 1.17 1.11 1.01
1981 1.70 1.34 0.97 1.14 1.05 0.96
1982 1.78 1.38 1.03 1.21 1.16 1.02.
1983 1.78 1.43 1.03 1.31 1.19 1.17'
1984 1.84 1.39 1.09 1.31 1.32 1.24
1985 1.82 1.26 1.31 1.37 1.20 1.43
lIean 1.69 1.24 1.11 1.08 0.97 0.80
Table(3-36): Injury rate per unit
population after log transfor.atlon.
Year RYH HKH DAM HRT QSH SUT
1971 0.95 1.04 0.87 0.85 0.59 0.34
1972 1.11 1.06 1.16 1.05 0.95 0.43
1973 1.23 1.17 1.13 0.98 1.10 0.58
1974 1.14 1.25 1.24 1.08 1.11 0.51
1975 1.37 1.31 1.29 0.97 0.88 0.66
1976 1.43 1.37 1.10 1.00 1.01 0.70
1977 1.40 1.28 1.22 1.10 0.86 0.76
1978 1.39 1.42 1.37 1.21 0.99 0.91
1979 1.35 1.46 1.39 1.20 1.15 1.15
1980 1.45 1.43 1.18 1.11 1.15 1.10
1981 1.39 1.43 1.05 1.17 1.23 1.00
1982 1.40 1.49 1.18 1.20 1.29 1.09
1983 1.33 1.56 1.20 1.39 1.37 1.11
1984 1.42 1.50 1.24 1.32 1.44 1.11
1985 1.36 1.41 1.40 1.37 1.34 1.29
lean 1.31 1.35 1.20 1.13 1.10 0.85
Table(3-37): Fatality rate per unit
..'population
after log transfor .. tlon
,
Year RYH HKH DAM NRT QSH SUT
1971 -0.16 0.16 0.11 0.00 -0.22 -0.70
1972 0.04 0.29 0.36 0.04 0.00 cO.70
1973 0.08 0.40 0.34 0.18 0.04 -0.22
1974 0.15 0.36 0.41 0.20 0.34 -0.30
1975 0.36 0.48 0.58 0.32 0.20 -0.16
1976 0.34 0.59 0.54 0.39 0.46 0.04
1977 0.51 0.57 0.53 0.34 0.32 0.011
1978 0.36 0.66 0.56 0.48 0.38 0.28
1979 0.28 0.66 0.67 0.52 0.58 0.51
1980 0.40 0.63 0.63 0.53 0.48 0.36
1981 0.28 0.59 0.57 0.49 0.46 0.17
1982 0.32 0.70 0.46 0.52 0.65 0.34
1983 0.34 0.69 0.52 0.60 0.65 0.32
1984 0.34 0.64 0.54 0.53 0.66 0.26
1985 0.34 0.54 0.65 0.57 0.57 0.49
aean 0.27 0.53 0.50 0.39 0.37 0.05
60
..
Table(3-36)
source of
, ANOVA table for the different regions of Saudi
Arabia per unit population ( X 10000) atter log
transformation.
variance
d. f.
S.S.
H.S.
F
For the accident rate:Due to Years
14
2.91603
0.20629
11.09
5
6.94234
1. 36647
73.69
Error
70
1. 31499
0.01879
Total
89
11. 17336
14
2.21682
0.15834
11.38
5
2.39772
0.47954
34.45
70
0.97429
0.01392
89
5.58883
14
3.64001
0.26000
17.43
5
2.29401
0.45880
30.76
Error
70
1.04420
0.01492
Total
89
6.97822
Due to Regions
For the in1ury rate:Due to Years
Due to Regions
Error
,
Total
For the fatality rate:Due to Years
Due to Regions
61
..
Table(3-39): Uuncan's Multiple Ran~e
Test for the regions of the
accident rate per unit population ( X 10000 ) atter
log transformation.
For
cl
= 0.05
2
2.83
0.0999
r
R
3
2.96
0.1051
4
3.07
0.1064
5
3.14
0.1109
6
3.20
0.1129
~egion
South
Qaseem
North
Dammam
Makkah
Riyadh
Means
0.7954
0.9702
1. 0750
1.1092
1.2436
1.6874
sels of 2
No further sets could be deduced.
For
0( = 0.01
r
R
2
3.75
0.1325
3
3.91
0.1382
4
4.02
0.1420
5
4.10
0.1447
6
4.17
0.1470
Region
South
Qaseem
North
Dammam
Makkah
Riyadh
Means
0.7954
0.9702
1.0750
1.1092
1.2438
1.6874
sets of 2
No further sets could be deduced.
62
Table(3-40), Duncan's Hultiple Range Test tor the regions of the
injury rate per unit
population ( X 10000 ) after
log transformation.
.
For
0(
=
0.05
2
2.83
0.0860
r
R
3
2.98
0.0904
4
3.07
0.0933
5
3.14
0.0954
6
3.20
0.0972
Region
South
Qaseem
North
Dammam
Riyadh
Hakkah
Means
0.8509
1.0967
1.1331
1.1996
1. 3145
1. 3450
sets of 2
No further sets could be deduced.
0(
For
=
0.01
2
3.75
0.1141
r
R
4
4.02
0.1222
3
3.91
0.1189
5
4.10
0.1246
6
4.17
0.1266
Region
South
Qaseem
North
Dammam
Riyadh
Hakkah
Mean.s
0.8509
1. 0967
1.1331
1.1996
1.3145
1.3450
set.s
of
sets 01
No
2
3'
turther
sets could be deduced.
63
Table(3-411: Uuncan's Multiple Range Test for the regions of the
fatality rate per unit population ( X 10000 I after
log transformation.
For
0{
= 0.05
r
R
2
2.83
0.0890
Region
South
Riyadh
Qaseem
North
Dammam
Makkah
0.0519
0.2659
0.3717
0.3815
0.4998
0.531.8
Means
3
2.98
0.0936
4
3.07
0.0966
5
3.14
0.0988
6
3.20
0.1006
sets of 2
No further sets could be deduced.
For
0(
= 0.01
r
R
2
3.75
0.1181
Region
South
Riyadh
Qaseem
North
Dammam
Makkah
Means
0.0519
0.2659
0.3717
0.3815
0.4998
0.5318
3
3.91
0.1231
sels of 2
sets of
5
4
4.02
0.1266
3
No t-urther sels could be deduced.
4.10
0.1289
6
4.17
0.1310
64
TableI3-42): Duncan's ""Itiple Ran!e Test for the years of the accidents rate per unit population ( I 10000) after ID!
transf orut i on.
ror
0::
= (;,(;5
2.83
r
Fi
Tear
1,71
'.I. ':~.
Means
set:
:or
.1
set: of :.
set: c-': -:
,~
10'"
.• ~(,:
3
4
2.98
3.0;
5
3.14
3.20
0.1061
0.1714
0.1753
0.1785
(;.~751
1,,,,
1:;;4
!. ':·lE,:·
1975
19;0
1.148,
1981
7
8
9
3.24
0.1811
3.28
3.31
0.183,·
0.185')
19i8
1.:1 ;7
19i9
1980
1
...,
~"':.
, . o!:."t, I)
1962
1.2bl0
198,·
1. :'19C~
O.186~
1984
1985
1. 3648 1.';':;76
65
Table(3-43): Dune.n'. "ulllple Rance Tesl lor lhe year. 01 lhe Injury rale per unll populallon ( 1 10000) alter log
transfor.ation.
Fat'
0:
'.
= 0.05
,
3
'-
:.8~·
r
F.
(J.136(1
lea,'
lS;1
Mean:;
(:, ;:S~
:Ets of
-
sets of
-'
tt?7::
0. S-58~
2.96
4
3.0i
0.1430
0.14ib
11:":'"1'
• I .'
19i4
1.0296 1. O:'5~
set: of 4
set; of
•0
sets of
,
set.; of
-.
se t;: "'
-
!
Nc:' fw"tner set: CDIJld be
oeou·:ec.
1975
1.079,
S
3.14
0.1509
1970
I.IO(,e
19i7
1.02~·
b
3.20
7
8
9
3.24
3.28
0.1537
0.ISS9
0.1578
3.31
0.1593
1981
1978
1.2107 1.2IS\
198(,
1. 2367
1982
l.me
1979
1. 2840
,1t)
"
..,', <J.J
0.1605
1983
1964
1985
1.3267 1.3385 1. 3bOS
66
..
·ableI3·4.): Dunean's Multiple Ranle Test for the years of the fatality rate per unit population ( I 10000) after 101
transforaaUon.
I
a:
For
= v.05
2
2.63
0.1408
I,.
R
,
:2.98
0.148('
I c·-:"\
1""C,
1973
-0.132:;
V.e'('ot O.136 i
"eans
lear
set;
4
3.07
0.1526
"
,
v
set= of 4
sets 01 •.;
set; of
0
set:; wf 7
sets of 8
set; CoT
Uo
tu~·ne
0
3.20
0.1591
7
3.24
0.1014
8
3.28
0.1033
9
3.31
0.1049
1(,
3.3-3
0.IOb2
1975
197;
1963
1974
1977
19ib
1981
1984
1982
1985
1978
1980
0.1;46 v.2963 0.3915 0.3908 0.4286 0.452:, 0.4957 0.4992 O.505i 0.5217 O.524S- 0.5304
or --.
sets of
5
. 3.14
0.1502
"
sC?{: i:odd tiE aeO'li:eu'
67
Pig. (3 -
,1)
Monthly accidents, injuries, and fatalities in Saudi Arabia
for 1974 - 1985
3000
2500
~
::"
'.
"
2000
::
",
fil!
. ,:.'r~
"
""
{,
"
...
:::
i1rv
iVr i\;"
..
:: ....
1500
[J
::"
,
::::
~;
\.~:
....
f~
1000
500
Legend
accidents
04-~_r
•
o
20
40
60
80
months
100
120
140
160
o
!i\J.~"
•
fatalities
..
68
Fig. (3 -
~)
Monthly accidents, injuries, and fatalities in Riyadh region
for 1974 - 1985
1400
1200
1000
800
600
400
Legend
200
O~-
o
20
40
60
80
months
100
120
140
160
•
accidents
o
Injuries
•
fatalities
69
Fig. (3 - 3 )
Monthly accidents, injuries, and fatalities in Makkah region
for 1974 - 1985
1200
:
I
1000
:
.
f:
::
n
lj l
800
j ff
J : 1:
:: ::
$::
::::
,"
(:::
::::
::::
: :::
o
,."
"
'."'. ..
600
.......
~.,'
400
il/
;: :~:';
.:
.::.
"
I
~
.....
'"
': :::
:
'','.
"
~.
~
.~
,
,"
,"
,"
Vr i f::
....
J ::
" .,
"
,'
::
I\,
V
.. ,.
'.
:::
...'.':: ,r
··, .'
I:i \1 ! .'.'.'.'
· ..:: ::: :
i V'
:.
;
.
...'
..:~..'.. '
:'
'
1
.
'"
200
. Legend
•
accidents
O~-r.'
D !"I~Xis
•
o
20
40
60
80
months
100
120
140
..
160
.....
fatalities
70
Fig. (J -
4)
Monthly accidents, injuries, and fatalities in Dammam region
for 1974 - 1985
300
,,
.
."
.....
,
..'.'.' .."",.
:::
'
:~
'
",
:' ::
! ' :
~
j:: : ..
,'.. .
.......
' ,. .
,',0 •
......
,"
..
..,
..
:::
; ::
,"
...
,"
'"
r: ~ j
,"
j
...
,'., .
:::: :
:::: :
."
," . "'
,"
200
;
~ ~
,'"
,,',
,",
,",
,",
.."
250
. El..
!
i
.
',.
'.'.'.
'.
'.
'.
'.
150
::
n
MW'
..
100
. ",'.
:
!~·"1,
'.
::
:~
/i
:.~
::
.,' "
,'"
:::
(
50
Legend
•
occidents
O~-r.',
D !'[~.riE
•
o
20
40
60
80
months
100
120
140
160
....
fatalities
71
5)
Fig. (J -
Monthly accidents, injuries, and fatalities in North region
for 1974 - 1985
450
,
,,
400
,
350
"
.,
300
, ""
.""I~ ../~
'"
'"
, "
:':::"~
r
'
250
l
::
,I
::
"
::::
200
':':,
,
,
,
150
i, ~:
~
"
, 1
Ni
;
i
~
, '
::
::
':v
"
n
1:;\:
)1:1
.. ..
: ~;'
100
W
!
, '
: ~: : :
....
:
:- :
:: ::
\
~ U
,
,,
. ;.
""
Legend
50
O~-.r
o
20
40
60
80
months
100
120
140
160
•
accidents
o
!~iu,r.
•
fatalities
72
Fig.
0 -
6)
Monthly accidents, injuries, and fatalities in Qaseem region
for 1974 - 1985
250
I,
!
f\ ~ ...... ~
200
:
,:
I ,.
150
.
:
..
··:' .: \ ~V f
100
'"
·
····
·
"
.,
.,
.,
.,
I
.,
.,
.,
::
::,'
'.
50
Legend
•
•
accidents
O~-r.'
0 !'l~.ri
o
20
40
60
80
months
100
120
140
160
....
fatalities
73
Fig. (J - 7 )
Monthly accidents, injuries, and fatalities in South region
for 1974 - 1985
600
500
400
300
200
100
Legend
O~-.,
•
o
20
40
60
80
months
100
120
140
160
•
accidents
o
!~i.r
•
fatalities
....
74
ACCIDtM'fS
'~IJ\lES
""<>
~
___ •
___ o n
JAtAl,I":IE! ----
~
lliiliffi
m
<00,
",)0
)000
2000
'000
iU.1OW1
Fig. (3-8a):Accidents,injuries,and fatalities of Saudi Arabia for 1973.
z~o
:-.C't'O
"'00
.:!2~O
'111)00
ACCIl!ttl" _______
~
i :,1
I1lJUlltr.8---- _____
[TIJlIJ
!
F"TAl.ITn:;-------
~
I:
20000
, 9':000
,I:
!I
"'''''''
170':0
I
'600'
IS000
"COO
1)000
':>;mo
11000
,<=
''lOO
80'..0
,0«>
""'"
,000
i
;
I
'I
I
,I.,
Iq
d.
Ht
,I
11.
'0;
'I
p!.,
i,
: II
: 1I
4f),)'J
)000
',<>GO
'000
SA\JtII Ar.ABlA
RlnD11
Fig. (J-8b) :Accidents, injuries. and fatalities of Saudi Arabia for 1983.
72
69
66
6)
ACCIDEJlT RAtB ---INJURY RATE -----FATUI'l'Y RATE ----
§
UIII11
mm
60
57
54
51
4.
45
42
)9
--.J
)6
\J1
))
)0
27
24
21
,.
15
~
12
9
6
)
SAUDI ARABIA
Fig. 0-9)
RlYAIIf
KAKKAH
Ill"".
QlSEEIA
Accidents,ir.juries,and fatalities rates per 1000 vehicles for
an average of 15 years (1971-1985).
SOUTH
76
"140
m.ruRY RJ.tE - -
135
PATA.UTy RATE -
130
m
FOR llJ AVERAGE 0' 15 n:.lRS.
125
120
11,
"0
10,
lOO
9,
90
.5
eo
75
70
.,
60
55
'0
4'
40
)0
25
IR
I
20
"
10
,
~
ttm
SAUDllJU.BI1
mm
Ilm
.
tjfflj
NORT
•
...
SEE
Imm
so\J'1'II
Fig.(J-10): Injuries and fatalities rates per 100 accidents for
an average of 15 years (1971-1985).
77
CHAPTER IV
APPLICATION OF REGRESSION ANALYSIS
4.1
INTRODUCTION:-
Selecting appropriate models by using the regression analysis
procedures
can be done
in various ways
according
to
the
adopted
method of regression.
In this chapter we are interested in finding the best subset
of regression models for a given three response variables and seven
predictor variables by using four different regression procedures.
The study of road traffic accidents depends on many variables
as described in Chapter Ill.
Application of regression analysis in modelling number of road
traffic
accidents
Y1,
injuries
Y2
and
fatalities
Y3
for
the
different regions of Saudi Arabia and to Saudi Arabia overall can be
done for any set of regressor variables.
But in this study we are
hindered by the availability of insufficient data for this kind of
analysis, i.e. the available data !DUst be for a long period to give
better model fitting.
For this reason we have been limited to seven
predictor variables and three response variables as mentioned above
for
a
period
of
15
years
described in section 3.4.
(1971-1985)
for
the
yearly
data
as
78
The response variables are:Number of the yearly road traffic accidents, and denoted by 11 ,
Number of the yearly resulted injuries, and denoted by Y2,
Number of the yearly resulted fatalities, and denoted by Y3.
The predictor variables are:Population size based on estimation as given in Appendix A,
and denoted by X1 ,
registered vehicles up to the
Accumulated number of the
given year , and denoted by X2,
Number of the newly issued driving licences each year, and
deno ted by X3,
Number of the newly registered transport vehicles each year
and denoted by X4,
Number of the newly registered private vehicles each year, and
denoted by X5,
Number of the newly registered taxis each year, and denoted
by X6,
Number of the newly registered buses· each year, and denoted by
X7.
The data of the above variables are given in Tables (3-12) (3-18). These variables cover the main re'l.uirements of' the proposed
statistical analysis in this Chapter.
The regression analysis is restricted to the following
regression methods.
R2 criterion "The coefficient of determination", by using
Aitkin's ade'l.uate subset approach.
Backward elimination procedure
Forward selection procedure.
Poisson regression by using the iteratively reweighted least
s'l.~are
approach.
In the next section we describe our regression models and
We also introduce a theoretical background to
their parameters.
of
help justifying the analysis and in giving a better und~rstaig
the results.
79
A brief note on testing the residuals for any regression model
is introduced in Section 4.4.
regression models for
regression methods.
the
This tes t will be used for selected
best
subsets
Sections 4.5 and 4.6 will inclucie
cri terion and
procedures
the
used
backward
in
by
the
the'
previous
a description of the R2
elimination and
finding
using
the
appropriate
forward selection
models.
The
fitted
models and the best subset of each region also will be included.
Poission regression will be appl "Len in fi tting the number of
road traffic accirients J injuries and fatalities in Saudi Arabia, as
an application of this
kind of models.
Description and
fitting
models by using Poisson regression is given in Section 4.7.
The
iterative reweighted least squares approach and the log likelihood
test statistic are used.
4.8 to
Section
see
The dummy variables technique are used in
if
there
are
any
differences
between
the
different regions, where the dummy variables deal with all the data
as one group_
in Section 4.9
Finally
we
make
a
comparision
between
the
different regression methods which are used, in addition to results
and discussion about this chapter.
4.2
THE REGRESSION MODEL:The multiple linear regression models will
study.
be
used
in
this
Consider the model,
y'
J.
= n
1
"'0
X0
i
+
p1 Xl i
+
+
P X 2.
+
P6 X6 i
+
2
I
P3 X 3.
+
P7 X7.1
+
I
P4 X 4.
I
+
P5 X \
( 1)
f.
I
where
i
=
1, 2, •••
, 15 represents the number of years considered
for the analysis.
j = 1, 2, 3 denotes the three response variables Y1, Y2, and
n. as
XO:
defined in section 4.1
is a (15x1) vector of one's representing a dummy variable.
X1, X2,
, X7: denotes
in section 4.1
the seven response variables as defined
80
~o
'~I
~7
""
are unknown parameters to be estimated by the least
:
squares me thod,
is
E,
the
error
term
a
is
which
•
distributed with zero mean and un~ow
random
variance
normally
variable.
0'
•
i. e.
€
N (0,0')
-
Relation (1) can be expressed in a matrix form as follows: Yj
~
X
+
( 2 )
E
where
) vector, and j
Yj
is a (15 X
X
~
is a ( 15 X 8 ) matrix,
) vector,
is a ( 8 X
E
is a ( 15 x
At
this
stage
1 • 2. 3.
) vector.
we
are
going
to
find
regression models that fit, the given three
the
best
subset
of
response variables for
each of the six regions of Saudi Arabia and Saudi Arabia overall.
seven subsets of the best regression equations.
So we have
each of which consists of three models to fit the number of accidents
Y1. injuries Y2. and fatalities Y3·
4.3
THEORETICAL CONSIDERATION:There
are
some
statistical
indications
and
tests which are used
mainly to find the appropriate models. :10st of these will· be ciescribed
in brief notes according to
simple linear models. then the idea
will be generalized to a multiple linear regression model (using a
ma trix form).
4.3.1 LEAST
SQUARES METHOD:-
This method is·
used
regression equation ~;".
to estimate the parameters of a given
The
method
of
least
squares is
simply
minimize sum of squares of the difference between the observed value
A
the
predicted
value Yi·
Let
S denotes
between' the obserVed and predicted values.
observations
as
follows
(X1'
Y1).
(X2'
this
difference
n pairs
(Xn •
Then for the simple linear model
Y
i
='{3
0
+{3
1
x
I
+E
i
( 3 )
81
we have,
Min
~
S = Minimize
"" 2
n
E = ~
n
i=l
,
,......
2
( y. - ~ - ~
X. )
".. 2
,
(y.-y.)
j=l
I
1
0
( 4 )
I
The general linear model of (3) can be put in a matrix form as
y
( 5 )
In order to minimize S i t is necessary to take the partial
derivative of S with respect to each
~
,set each of these partial
equations to zero and solve the resulting equations simultaneously,
the resulting equations are called the normal equations.
the
In
case
of
simple
a
linear
the
regression,
normal
equations are
+
b n
b
0
~x
b
= ~
~x
J
+
y
b
2
(6 )
~ x, =
J
0
x.,
~
y
where bo and b1 are the estimates of flo and fl1 respectively by
using the least squares method and n is the total number of
observations.
By solving equations(6) we find that
x. y. ~
I
I
2
~x
b
o
;
-
(~x.
I
~
~x)
Y. )
I
2
I
~(x.-X)
n
,
(Y.-Y'
,
(7 )
In
Y'
(8 )
Substitute
equation
(8)
into
equation
(3),
the
estimated
regression equation will be
(9)
The normal equations in a matrix form will be
XXb
---
,
=
XY
(10)
82
where
I
X X
,
x
Y"
and
b
=
equations of (10) multiply the both sides
To solve
I
by
(!!)
-1
,where
(X X )
,
n :!: (X, -
-
X )
2
we obtain
,
(!!)
[
-1
I
-I
b
(!!)
=
-
:!:x
n
:!: X
]
-1
I
I
(!!)
-
XY
that is,
,
b
, 1
Where (XX)-
From
=
-1
(X X)
,--
(!!) =
equations (11)
,.
I
(!!)
( 11)
I , I is the unit matrix.
and (5) we found that
(12 )
Y = X b
4.3.2 ANALYSIS OF VARIANCE TABLE:
To see the precision of the estimated regression line consider
the following identity,
( Yi - Yi ) = (Y i or
-
y)
- ( Yi - Y )
-
,.
( Yi - Y ) = (Y i - Y)
,..
+
(Yi - Y)
both sides of (13) and take the summation over all the
Squaring
values fTom 1 to n, and simplify, we found that
2
:!: (Y, -
•
Y )=
,..
_ 2
+
:!: (Y, - Y)
•
2
~
,
,
:!:(Y,-Y,)
( 14 )
83
where t
_2
Y)
is
the
sum
of
squares
of
deviations
of
the
observations from the mean, and denoted by SS about
the mean with (n-1) degrees of freedom (d.f.).
_ 2
Y) : is the SS of deviations of the predicted values from
the mean, and denoted by SS due to regression wi th 1
d.f. (in the case of one regressor variable).
~
'"
2
(Y i - Y.): is the SS of deviations of the observations from its
predicted values, and denoted by SS of the residuals
with (n-2) d.f.
Equation (14) can be expressed in the words as follows:
SS about the mean
=
SS due to regression
SS of the residuals
+
The mean square is given by dividing each sum of squares by
its corresponding degrees of freedom.
The above notes can be summarized in the analysis of variance
table (or AN OVA table for simplicity) as given in Table (4-1).
Table (4-1)
AN OVA table for the simple linear regression
Source of Variance
Due to Regression
Residuals
Total
d. f.
Sum of squares
0
1
~
n-2
n-1
'"
(Y.-
•
~
i=l
0
i=l
Y)
,.
2
2
(Y. - Y.)
I
I
0
r
i=l
(Y - Y )
I
Mean square
2
MS
2
•
=
R
=
SS
MS R
I
•
-SS
0-2
F-Value
2
84
s2, the mean square of the residuals, is sometimes called" the
mean square error and denoted by MSE.
In a general regression case
if we have p-regressors and n observations, the ANOVA table in this
case will be as in Table (4-2).
Table (4-2)
ANOVA Table for the general regression case
Source of Variance
sum of squares
d.f.
Regression
p
Residuals
n-p
Total
, ,
b XY
--- , ,
1'Y - b X Y
----
Mean square
MS
R
12 =
=
F-Value
MS R
ss
p -
,2
ss
--
.-p
I
n
YY
--
4.3.3 F-TEST FOR SIGNIFICANCE OF REGRESSION:
From Table (4-1) the calculated F-value for simple regression
_
~
F
=
MS R
,
~(Y.-)
~
,2
hence the
, V.,
(15 )
)2 / ( • _ 2 )
will follow- a
distribution
will follow.
ratio F
~s
/1
( y. _
2
The MS R divided by 0
and also (n-2)s2 divided
tribution,
2
MSR/s2 will
a
2
X
('-2)
dis-
follow the F-distribu-
tion with (1) and (n-2) degrees of freedom.
For the general regression case the calculated F ratio will be
F
( 16 )
,2
a"nd the -test will be III
wi th F ( ex:; p , n - p ).
=
Il2 = ... = Ilp
= 0,
by comparing F = I~SR/s2
g~ven
by
85
4.3.4 THE COEFFICIENT OF DETERMINATION "R2"
For any regression line, all the observations do not usually
lie on this line.
be zero.
If they all did, the residual sum of squares will
More generally, we saw that a fi tted regression line is
likely to be of practical use if the mean squares due to regression
is much greater than the residual mean squares, or if the ratio
R2
=
SS due to regression / SS about the mean
is not too far from unity.
n
-y )
i=l
2
R
n
r
So
::l
"y
r
(17)
y. I
i=1
..
Y)
( 18 )
or, equivalently, in matrix form
,
_2
I
~r
2
( 19 )
_nV
,
R
-2
Y Y _ n Y
This
ratio
R2
is
called
coefficient or coefficient
proportion of
total
the
squared
of determination,
variation about
the
multiple
and
it
correlation
measures
the
mean Y explained by
the
regression.
In this chapter we use
models,
to
find
the
bes t
the R2_criterion for a given set of
model
approach to fit the given data.
by
using Aitkin adequate
subset
This procedure will be discussed
later.
Adjusted
R2 _criterion
is
denoted
by
R2
and
defined
in
correspondence to R2 as follows:
R2
•
where
.
=
n is
1-
the
(i - R
2
n -
)
1
( 20 )
n-p
total number of observations
number of parameters in a model to be estimated.
and
p is
the
total
86
R~
is a statistic adjusted to take account of the number of
regressor variables and the number of cases.
vative
estimate
of
the
"explained"
It is a more conser-
proportion
of
total
sum
of
squares than R2, especially when the sample size is small.
R2a values are included in the tables of fitted models only,
but not used in the analysis.
The figures of R2 are given for any
further studies about this subject.
4.3.5 PARTIAL F-TEST:Partial
F-test
will
elimination procedure.
be
used
in
describing
the
backward
.Brief details of this test can be given as
follows.
If we have a regression model with several terms, we can think
of these terms as "entering" the equation in any desired sequence.
So we find the extra sum of squares for the estimated coefficient
b i given other coefficients in the model, i.e.
So we have a sum of squares on one degree of freedom which
measures the contribution to the regression sum of squares of each
coefficient b i given that all the terms which did not involve
ili
which were already in the model.
In other words, we shall have a
measure
of
the
value
of adding a
il.,
term
to
the
model
which
originally did not include such a term.
The corresponding mean square, is equal to the sum of squares
and since it has one degree of· freedom, can be compared by an F-test
to s2 as given in section (4.3.3).
This type of F-tes t is called
a partial F-tes t for ili .
When we build a sui table model the partial F-tes t is a useful
criterion for adding or removing terms from the model. The effect of
87
an X-variable (X p say) in determining a response may be large when
the regression equation includes only Xp'
However when the same
variable is entered into the equation after other variables, it may
affect the response very little, due to the fact
that Xp is highly
correlated with variables already in the regression equation.
The partial F-test can be made for all regression coefficients
as
though
each corresponding variable
were
the
last
to enter
the
equation to see the relative effects of each variable in excess of
the others.
When
the
variables
are
added
one
by
one
in
stages
regression equation, we can talk about a sequential F-test.
to
a
This is
just a name for the partial F-test on the variable which entered the
regression at that stage.
4.3.6 PARTIAL CORRELATIONS:These
procedure
are
in
important
section
in
4.4.
describing
Sometimes
the
we
need
variables one by one to the postulated model.
forward
to
add
selection
predictor
The first predictor
variable placed in the postulated model is chosen as the one which
is most correlated with Y,
tion coefficient
is X,.
*
X3'
of
r,
lY
The model
gressing it on X"
on X"
Y* and
respectively.
~
+~
0
then
regressing
2
~
y=
*
fitting the model X =
is
the variable Xj whose correla-
the largest of all r
Xp are
X2 after
that
it
I'
+~
1
X
1
+e ,
X
011
X"
that
I
+ e ,
, ,2, ••• ,p,
is fitted.
constructed
on
I =
ly
by
New variables
finding
is,
the
suppose
the
residual
residuals
from
the residuals of X3 after re-
the residuals of Xp after regressing it
The
values
the new predictor variables
of
*
X2'
the
new
dependent
*
Xp
variable
represent
those
portions of the corresponding original data vectors which have no
dependence on the values of the variable X,. Now we can find a new
88
set of correlations which involve the starred variables. These are
called partial correlations and can be written, for example,
meaning the correlation of variables X2*
and Y* and
partial
Y after
correlation
of
variable
X2 and
read as
both
have
"The
been
adjusted for variable X1· ...
In the second stage of the selection procedure we should add
the variable Xj to the model whose partial correlation coefficient
,
was
jy. J
Xj
most
that is,
the greatest;
correlated
with
we should choose
after
Y
the
effect
the variable
X1 has been
second X variable
of
Xj •
If the
selected in this way is X2 Say, the third stage of the selection
procedures involves partial correlations of the form '. 12' that is
IY·,
both
removed
the
from
and
Y
correlation between
X2 and
the
residuals
from
the
residuals
of Y regressed
of Xj
on X1
regressed on X1 and
and X2 • This process
can be continued to any extended desired.
The partial correlation can be expressed in terms of simple
correlations, for example
,
2y.1
( r
v(
2y
-
r
12
1 _ ,2
•
)
Iy
r
l y
( 21 )
( 1 -
,
2
12
and in the general case
,
ij .,k
,
ij
-
,;k
V( 1 _ ,2;k
,
jk
( 1-
,2
jk
( 22 )
89
4.4
TESTING OF THE RESIDUALS:-
The residuals are defined as the n differences ei =
A
Yi
-
Y
n where Yi is an observation and Yi is the
correspondence fitted value obtained by using the fitted regression
for i = 1, 2,
,
equation.
So the
residuals
ei are
the
differences
between
the
actual
observation and its predicted value by the regression equation.
Yi
=
There are certain assumptions for the residuals, for the model
xj + €.I
i = 1, 2, •••. , n.
~o
+ ~l
The assumptions are:
1 -
E.
I
is a random variable with zero mean and unkonwn
variance
2 -
E.
.1
is a normally distributed with zero mean and variancecr1.
that is
3 -
E.
I
and
E.
J
E
j
-
N ( 0,0-' )
are uncorrelated, so Cov (e., E.)
1
J
The following methods are given to examine the
order to check the validity of the given model.
=
0, for i "f J
residuals in
These methods are
given in the following:
1 -
Time sequence plot of the residuals:
then the
plot will
be a
If the model is correct,
rectangular scatter around
a
zero
horizontal level with no trends at all.
~
2 -
Plot of the residuals against the predicted value Yi' here
we look for the patterns.
good fit for the model.
The absence of which indicates a
90
3-
Plot of normal scores of the residuals against the residuals
itself. By this plot we can check for the normality of the
residuals.
The t tb normal score is defined to be the
(t - 3/8) / (n + 1/4) percentage point of the standard normal
distribution, where n is number of the observations, a plot of
the residuals agains t
the corresponding normal scores should
fall approximately on a straight line if the
residuals are
normally distributed.
4-
Durbin-Watson statistic, which utilizes the fitted residuals
n
2 n
2
and is computed as d = ~
(e t - et 1) / ~
et. This is comt=2
-
t=1
pared wi th upper and lower bounds d Land d u
for various
values of n and various numbers of input variables.
I f the
presence of serial correlatiotl is suspected,
model to explore is given by
E_
1
= P E_
1-1
a simple firs t
+ 0_ , where the 0_1
1
are uncorrelated and normally distributed.
the serial correlation amongst the
E_
1
If the degree of
is large (i.e. p*l )'
this will lead us to consider taking the first differences of
the residuals.
Thus we could plot
E.
1
-
E.
1-
Ivalues (or their
fitted equivalent values) and consider whether these points
can be considered to be randomly dis tri bu ted.
recalculate
the
Durbin-Watson
statistic
for
We could also
these
first
differences.
This
statistic
successive values of
is
Ej
used
to
determine
whether
the
are correlated. In this case we have
serial correlation, and its presence can be detected by the
above procedure.
91
4.5
REGRESSION ANALYSIS BY R2 _ CRITERION:
In the following we are going to describe Aitkin's adequate
subset approach by using the coefficient of determina tion R2 as a
cri terion for finding the best subset amongst all the possible subsets of regressor variables.
This approach is briefly described in the following:-'
Consider the regression model Y = X (3 + e
X is
vector,
unities, and
1.
nx(p+1)
matrix
of
full
is (p+1 )x1 vector, where
.!
parti tioned in such a way that
=
!.I -E.,
rank
X
+
and
where
with
.!
is (nx1)
first
column
{3 are conformably
!2.Pi +
e. That is to
say the variable subset of interest for inclusion will make up the
columns of the
!,
matrix,
and the variables being considered for
omission make up the columns of
X2
Here we construct a simultaneous test for all the subsets of
X.
This test does not reject
R2 _
Ho:(3 = 0 for any subset if
R2
X
X
(1-R
or
R2
>
R2 =
o
2
x
I
)
/(n~
<p.F( 0:;p,n-p-1)
( 23 )
p-1)
1- { 1- R:} { 1 + p. F (0: ; p, n - p -1) / ( n - p - 1 )}
( 24 )
where
2
x is the coefficient of determination of the model which includes
all the predictor variables.
R'
i x,
is the coefficient of ' determination of the model which includes
the set of predictors in
X1.
The set of predictor variables corresponding to X1 will be
called R2
adequate ( 0: ) set if the above 'inequality
satisfied.
is
92
For the different regions of Saudi
Arabia and Saudi Arabia
overall we are interested in finding the subset of minimal adequate
sets, which is considered as the best subset, given all the possible
subsets of the entire model,
those sets for which
R
2
>
where the minimal adequate sets are
2
Ra
but no subset of variables in X1 is
Xl
adequate.
7
With seven predictor variables
there are 2
=
128 possible
regression models corresponding to each response variable, so that
wi th three response variables and the seven predictor variables we
have 384 possible fitted models for each region of Saudi Arabia and
for the country as a whole.
By
adequate
using
the
ex
) sets
(
above
technique
( for given
we
ex
=
calcula te
all
the
0.05 ) for each response
From these R2 adequate ( ex ) sets
variable and for each region.
we find the minimal adequate sets by using the inequality (23).
The
resulting models of the minimal adequate sets are considered to be
the best subsets, given all the possible subsets of the regression
models.
The best subsets of the regression models,
subset
approach
in
addition
to
given in Tables (4-1) - (4-7).
d.f.,
R2,
R~
for Ai tkin' s
and
adequate
F-value
are
The computer Statistical Analysis
System package programmes (SAS) are used to carryout this analysis.
93
4.6
REGRESSION ANALYSIS BY BACKWARD ELIMINATION AND
FORWARD SELECTION PROCEDURES:
Here we use the backward elimination and
forward selection
procedures to find the best subset of the three response variables
and
7
regressor
variables
as
defined
in
section
(4.1).
The
technique will be applied only to Saudi Arabia overall, the Riyadh
region and the
We
need
region.
r~ekah
to
select
the
best
regression
equations
with
7
predictors, with 6 predictors, • -.. etc, under a determined level of
significance.
Backward
elimination
is
more
economical
than
all
the
regression methods in the sense that it tries to examine only the
best regressions containing a certain number of variables.
The basic steps in the backward elimination procedure are:.
1 2 -
3 -
A regression equation containing all variables is
computed.
The partial F-test value is calcualted for every predictor variable treated as though it were the last
variable to enter the regression equation.
The lowest partial F-test value, FL Say, is compared
with a preselected significance level F. say.
a)
If FL < Fa( remove the variable XL which gave
rise to FL and compute the regression equation in
the remaining variables, enter step 2.
b)
If FL > Fa( adopt the regression equation as
calculated.
.,
--------
94
So we cay say that the backward elimination procedure initially uses
all the variables, and subsequently reduces the number of variables
in
the
equation
until
a
decision
is
reached
on
the
desired
equation.
Note that the forward selection procedure goes from the other
direction,
that
is
variables
are
inserted
until
the
regression
equation is satisfactory, i.e., this procedure starts .nth the best
one variable equation and adds additional variables one at a time.
The order of insertion is
determined by using
the
partial
correlation coefficient as a measure of the importance of variables
not yet in the equation •
. The basic steps for the forward selection procedure are:1-
Take the predicted value X1, say, which is the most
correlated with the response variable Y and find the
first order, linear regression equation Y = f(X 1 ).
2-
If X1 is significant we search for the second predictor
variable to enter regression, by examining the partial
correlation coefficients of all the predictors not in
regression at this stage, namely Xi' i"" 1 with Y.
3-
The Xi with the highest partial correlation coefficient
wi th Y is now selected, suppose this is X2 and a second
This
regression equation Y = f (X1 , X2) is fitted.
process continues.
...
4-
As each variable is entered into the regression, the
overall regression is checked for significance, the
improvement in the R2 value is noted and the partial
F-test value for the variable most recently entered,
which shows whether the variable has taken up a
significant amount of variation. over that removed by
variables previously in the regression.
5-
When the partial F-test
recently entered variable
process is terminated.
value related to the most
becomes non-significant, the
-
95
By
using
a
computer
statistical
analysis
system
package
of programs (SAS), we found the best subsets of regression models by
the backward elimination procedure for given cr
=
0.1 in addition to
d.f., R2 and F-value are given in Tables (4-8) to (4-10) for Saudi
Arabia, Riyadh region and Makkah region respectively.
The
best
subsets
of
selection procedure for given
regression
cr
=
models,
for
the
0.1 in addi tion to d. f., R2 and
F-value by using the same package (SAS), are given in Table
for the same regions as above.
forward
(4-11)
96
4.7
FITTING A POISSON REGRESSION:
In this section we are going to fit a Poisson model to the
number of road traffic accidents in Saudi Arabia.
The data are
given in Table (3-12).
Let
Yl, number of accidents in Saudi Arabia, follow a Poisson
process with parameter
poisson model to
In the following we try to fit a
as a dependent variable and
Yl
Xl
(the popula-
tion size), X2 (number of the newly registered vehicles) and X3
(number of the issued driving licences) as regressor variables.
expected value of
I Xl,
E (YI
It
is
a
Yl
The
will be,
X2, X3) = P. = Ao + A,
linear combination of
Xl + A, X2 + A3 X3 •
the
predictor variables
( 25 )
and
the
parameters.
Hence we have the nonlinear regression model
f ( YI ; P. ) =
p.
YI
e
-p.
( 26 )
YI!
Estimation of the parameters Ao
'\
A, and
A3
' can be
calculated by using the iterative weighted least squares technique.
The Gauss-Newton iterative method
(or Taylor series
method)
is
applied by using SAS package.
This statistical package is required to specify the following
arguments to carry out the analysis of the nonlinear regression
models:
the
names
estimated.
and
starting values
of
the
parameters
to
be
97
2 3 -
the model (using a single dependent variable).
the partial derivatives of the model with respect to each
parameter A.,
i = 0,1,2,3.
1
For the first point we have the parameters Ao ' AI ,A,
A3 ,the ini tial values of these parameters are 126, 1.7, 1 .5
and
and
1.9 respectively.
For the second point the model defines the prediction equation
by declaring the dependent variable and defining an expression that
evaluates predicted values.
For
the
third
The model is given·in equation (25).
point
the
derivatives
are
given
in
the
following:
= 1 ,
at
= Xl
a AI
,."~_
ar
a A,
= X2 ,
The computer output is given in Fig. (4-9).
estimates
of parameters and
the
residuals
It includes
sum of squares
the
(SSE)
determined in each iteration until the convergence criterion is met.
The
iterations are said to have converged if
SSE.1 - 1
SSE.1 +
10
6
<
-8
10
at stage i.
The log likelihood ratio statistic D is used as inference to
measure the goodness of fit, as defined for Poisson model by Nelder
and Wedderburn (1972) to be
D = 2
fi=l
D
X'
Y 1. In ( Y1i.
1
'h
and
"v
(n- p)
ii.1 )
( 27 )
98
where
n
is
number
of
the
observations
predictor variables in the model.
will be larger than
of
the
Thus if the model is poor then D
=
1485.14, while X~2=
ments in the statistic
32.909 at 0.001
Other predictor variables are tried in the
(25) such as X4, X5, X6 and X7.
we
number
x (n-p)
level of significance.
Finally
p
2
From Fig. (4-9) we find that D
predicted model
and
D
conclude
But no improve-
are noted.
that
our
model
is
poor
and
Poisson
mode ling .is not sui table for predicting the number of road traffic
accidents in Saudi Arabia by using the above regressor variables in
th.e period of (1971 -1 985) •
So i t is arguable
that
this approach
cannot be sensibly pursued any further with the given data, and we
still need to deal with the linear regression models as given in the
previous sections.
99
4.a
THE USE OF DUMMY VARIABLES:-
Our concern
different
regions
is
of
to
look
Saudi
for
the
Arabia,
relationship
and
to
between
investigate
the
any
differences between them using the dummy variables technique.
We have six regions,
each one having 15 observations.
As
such, we have 90 observations and five dummy variables, denoted by
Dl, D2, D3, D4 and D5.
The yearly data set are formed to meet the
purpose of analysis and are given with their dummy variables in
Table (4-12).
For each of the response variables Yi
three
predictor variables,
namely,
(i=l,
2,
3) we have
the population size (Xl),
the
number of newly registered vehicles (X2) and the number of driving
licences issued yearly (X3).
The other four predictor variables,
which are given in the regression model (1), are omitted from the
dummy variables analysis, because from the earlier analysis it is
sufficient to carry out the analysis with the above three predictor
variables in addition to the dummy variables.
The following models are fitted for each of the three response
variables to see if there are any differences between the regions.
1 -
The saturated model which includes all the interaction terms
of the form,
b 1Dl + b2D2 + b3D3 + b4D~
+ b5D5 + b 6Xl + b X2 + ba X3 +
1
b (Dl Xl) + b l0 (Dl X2) + b ll (Dl X3) + b 12 (D2 Xl) + b (D2 X2) +
9
13
+ b (D4 Xl)+
b 14 (D2 X3) + b 15 (D3 Xl) + b 16 (D3 X2) + b 17 (D3 ~?)
la
= a ~
b 19 (D4 X2) + b20 (D4 X3) + b2l (D5 xl) + b22 (D5 X2) +,b (D5 X3).
23
100
The purely additive model with no interaction terms of the
2 -
form,
3 -
The regression mode 1 on the predictor variables only wi thou t
the dummy variables of the form,
"...
Yi = a + b
4 -
X3.
1
The regression model on the dummy variables only of the form
/'
Yi =
where i
1 , 2 ,
3
The above four models are fitted
to
the data by using the
Statistical Analysis System package programs (SAS).
The required
results are summarized in table (4-13).
Significance Test for Y1 :
First we test the null hypothesis of no interaction, testing
2648229/296326=8.937 as a random value from the F15,66distribution.
The test statistic is significant at the 0.001 level, so the null
hypothesis is rejected.
We conclude that there. is strong evidence of an interaction
effect and the saturated model is accepted. 'Hence the fitted
in this case will be
model
101
/'
Yl
2132 - 35843 Dl - 9560 D2
=
7532 D3 - 1196 D4 - 2957 D5
0.0015 Xl + 0.0166 X2 + 0.0741 X3 + 0.0332 Dl Xl - 0.0269 Dl X2 0.0092 D3 Xl - 0.0211 D3 X2 - 0.0612 D3 X3 +- 0.0010 D4 Xl
0.0068 D4 X2 - 0.0769 D4 X3 + 0.00)5 D5 Xl - 0.0138 D5 X2
0.0821 D5 X)
(28)
The fac t
tha t
the
F
test for interaction is significant
tells us that the effects of the explanatory variables differ from
region to region,
and in particular that no satisfactory common
model in terms of the explanatory variables only can be found to fit
all six regions.
By giving appropriate values to Dl,
saturated
model
we
obtain
the
six
D2,
D3,
separate
D4,
D5 in the
fitted
regression
equations appropriate to the regions under consideration.
/'.
Yl
33711 + 0.0317 Xl - 0.0103 X2 + 0.0257 X3
7428 + 0.0054 Xl - 0.0009 X2 + 0.0206 X3
(29)
r-
Yl
5400 + 0.0077 Xl
=
,...Yl
'"
Y1
=
'"
Yl
=
"Yl
(30)
0.0045 X2 + 0.0129
X3
(31 )
0.0028
0.0005 Xl + 0.0098 X2
936
825+ 0.0020 Xl + 0.0028 X2 - 0.0080
X3
(32)
X3
(33)
2132 - 0.0015 Xl + 0.0166 X2 + 0.0741
X3
(34)
Significance tests for Y2 and Y3:These follow along very
similar lines to the above.
The
test statistic appropriate to the null hypothesis of no interaction
is significant at the 0.001 level in each case (the values 4.077 and
4.323 respectively being tested as random values from the F 66dis15,
tribution). Thus the saturated model is appropriate in each case,
and the fitted regression equations will be
/'
Y2 =
0.0027
-
15172 Dl - 4877 D2 + 643 D3 + 6439 D4 + 3375 D5 +
~1
3457
+ 0.0001 X2 + 0.0450 X3 + 0.0147 Dl
0.0463 Dl
X3 + 0.0037 D2 Xl
+ 0.0020 D3 Xl
-
-
0.0028 D3 X2 -
Xl -
0.0060 Dl
X2
0.0002 D2 X2 -
0.0350 D2
X3
0.0271
0.0049 D4 Xl
D3 X3 -
+ 0.0116 D4 X2 - 0.0438 D4 X3 - 0.0017 D5 Xl + 0.0064 D5 X2
- 0.0719 D5 X3
(35)
102
together ri th separate regression equations for the six regions
/'
Y2
+
0.0100 X3
(37)
+
0.0179 X3
(38)
0.0022 Xl + 0.0117 X2 + 0.0012 X3
(39)
8334 + 0.0064 Xl
0.0001 X2
=
2814 + 0.0047 Xl
0.0027 X2
=
2892
"...
Y2
(36)
0.0059 X2
-
Y2
'"
Y2
0.0013 X3
18629 + 0.0174 Xl
=
/'
,,-.
Y2
82 + 0.0010 Xl + 0.0065 X2
0.0269 X3
(40)
3457 + 0.0027 Xl + 0.0001 X2 + 0.0450 X3
(41)
=
"...
Y2
=
and
.....
Y3
- 1079 - 506 Dl - 72 D2 - 433 D3 + 1370 D4 + 501 D5 + 0.0008 X1
- 0.0021 X2 + 0.0129 X3 + 0.0007 Dl
0.0118 Dl
X3 + 0.0001
0.0013 D3 Xl
Xl
+ 0.0016
Dl
X2 -
D2 Xl + 0.0019 02 X2 - 0.0069 02 X3 +
+ 0.0012 03 X2 - 0.0114 D3 X3 -
0.0037 D4 X2 - 0.0097 D4 X3 + 0.0004 D5 Xl
0.0010 04 Xl
+ 0.0019
+
05 X2
- 0.0092 05 X3
together with
A
Y3
rY3
r-
Y3
B
,...
Y3
rY3
=
= =
= =
= -
1585 + 0.0015 Xl - 0.0005 X2 + 0.0011 X3
(43)
1151 + 0.0009 Xl - 0.0002 X2 + 0.0060 X3
(44)
1512 + 0.0021 Xl - 0.0009 X2 + 0.0015 X3
(45)
291 - 0.0002 Xl + 0.0016 X2 + 0.0032 X3
(46)
578 + 0.0012 Xl
0.0002 X2 + 0.0037 X3
(47)
1079 + 0.0008 Xl
0.0021 X2 + 0.0129 X3
(48)
In an attempt to see whether a common model could be obtained
for some appropriately chosen subsets of regions for the above three
response variables, this procedure was repeated for a number of such
cases but each
significant.
time
the
interaction term appeared
to
be highly
It was therefore concluded that no such common model
was appropriate and the effects of the explanatory variables are
different for each region considered.
10)
4.9
RESULTS AND D1SCUSS10N:-
Various
authors
have
investigated
the
cause
of
accidents,
injuries and fatalities in Saudi Arabia by using some statistical
procedures such as analysis of variance and covariance,
classification and linear regression analysis
but
multiple
with different
regressor variables, Al-kaldi and Ergun, (1984).
The
variables introduced
in the
previous models
in
tables
(3-12) to (3-18) represent the important variables, because nearly
all of these models give a high percentage of R2 and less
0.05 level of significance
for
the F-test.
than
Other statistics in
tables (3-20) to (3-26) are also supporative of the argument.
Of course,
there are many variables other than the ones we
have used, such as,
the education level of the driver,
••• etc.,.
These variables are discussed in some studies in Saudi Arabia or
outside of it.
Some of these studies have been mentioned and the
importance of these variables have also been discussed in Chapter
11.
'lie have realized that most of these variables give unsatis-
factory
results
percentage
period.
for
of R2),
the
regression
because
the
analysis
available
data
(such
as
the
are
for
a
low
short
Therefore, we have ignored these variables in conducting
our analysis.
The basic statistics in tables (3-20)
-
(3-26)
relationships between the variables in the analysis.
explain the
We note that
the corr,Hation coefficient between the dependent variables Y1, Y2
and Y3 indicate strong positive correlation, as was expected.
104
The correlation coefficient between Yl and Y2 is the strongest
one which is 0.9818, for Yl and Y3 the value is 0.9541, and for Y2
and Y3 it is 0.9767.
These
figures
are
for Saudi
Arabia and
approximately the same figures hold true for the other regions, with
minor changes.
We
have
discussed
in
this
chapter
methods
of
regression
analysis to select the best model which fits a given set of data.
These methods are the R2 _criterion by using Aitkin' s ade'l.uate
subset approach,
selection
the backward elimination procedure,
procedure,
and
the
poisson
regression
by
the forward
using
the
iterative reweighted least s'l.uares approach.
Comparison between the regression methods which are used in
this Chapter.and discussion about the application of each method are
given in the following section.
4.9.1 AITKIN'S ADEQUATE SUBSET APPROACH:This approach selects the best subset of models by testing all
the possible subsets of the regression models for the given response
variable.
We have for each region a set of models as given in
Tables (4-1) -
(4-7) that is considered the best subset (minimal
ade'l.uate subsets) of models by using this techni'l.ue.
Most of the resulting models consist of two or three predictor
variables.
For all the best models, R2_values lie between 58% -
98% of the total variation for accidents, injuries and fatalities.
Also these linear regression relationships are significant at 0.001
level of significance.
105
For the different regions of Saudi Arabia we found that the
predictor variables
Xl, X2, and X3 are more frequently for the best
models of accidents, injuries and fatalities.
Checking the utility of a model can be done by testing the
"-
residuals ei = Yi - Yi •
The test procedures of the residuals
in section (4-4) are applied for selected models from t!"ie best
models of Saudi Arabia.
Durbin-Watson statistic will be used when
it is appropriate.
Durbin-Watson statistic
d
is calculated for the residuals of
each model of all the minimal adequate subsets in Tables (4-1) to
(4-7).
This statistic tests whether there is a serial correlation
in the residuals or not.
a
serial
correlation
residuals are
If We reject the hypothesis that there is
in a
model,
not correlated and
th1s
will
the model
indicate
fits
the
that
the
given data
well.
The starred models in Tables (4-1) to (4-7) indicate that the
d is
not
significant and
residuals of each model.
no serial
correlation appears
in
the
These models can be selected to be the
best models among all the minimal adequate subsets given in Tables
(4-1) to (4-7).
The models in Tabie
(4-1),
the minimal adequate subset
of
Saudi Arabia for the three response variables, will be selected as a
sample of
the study to make
the
test
of
residuals,
because
it
represents the overall situation of the country and its data are
general.
.,
106
According to the Durbin-Wa tson tes t of serial correlation of
the residuals, we have three test procedures as given below.
select
three
models,
_variables Y1,
if
any,
for
Y2 and Y3 represent
each
the
of
the
three
We
response
three test procedures
for
examination of the residuals.
In the following we are going to explain the test procedures
of the Durbin-Watson test, and select models for examination of the
residuals from Table (4-1).
Actually all the models which will be
selected are not all the models that met the specified test.
this tes t
the null hypothesis is Ho: no serial correlation appear
in the residuals.
.1
-
For
Ifd<
The test procedures are
d
d L ' concludes tha t
i.e.
rejected at level of significance
correlation in the residuals.
is significant and Ho is
there
is a
serial
In this case we select the following
models which meet this test,
Y1
ilo
Y2
ilo
+
il·l X2
+
il2
+
ill X2
+ €
X3
+
€
This tes t is not found for Y3.
2 -
If d
.>
du' concludes that
not reject Ho'
d
is not significant, i.e., do
and no serial correlation in
following models are selected to meet this test
Y1 = ilo
ill X2
+
Y2 = ilo + ill X1
+
Y3 = ilo
+
+
+
ill X1
il2 X6
+
€
€
il2 X2+il 3 X6
+ €
the residuals.
The
107
If d..
~
L
d
~
the test is said to be inconclusive, in this
u'
case, a simplified test are used, which is:
If d < d reject Ho
u'
other.ise do not reject.
The
at level of significance ~
3 -
d
following models are selected to meet this test,
11 = ~o
+ ~,
X2
+ ~2
X4
Y2 = ~o
+ ~,
X3
+ ~2
X5
Y3 = ~o
+ ~,
X1
+ ~2
X3 + E
\,here d Land
d·
u
are
+ ~3
Time
0(
series
Eo
+ E
the
Durbin-Watson test, respectively.
of significance
X5 +
lower and
upper bounds
of
the
The above tests are made at level
= 0.01.
plot
of
the
residuals,
plot
of
the
residuals
against the fitted response variable Yi (i=1,2,3) and plot of the
residuals against its normal scores are the three steps in examining
the residuals.
The first or second order difference will be used.
These plots are given in Fig(4-1) to Fig (4-8) and divided
into three groups according to the Durbin-Watson test as described
above.
Discussion about plots of each group are described in the
following:
Plots on models of the first group in which we reject Ho are
given in Fig(4-1) and Fig(4-2).
The
residuals do not behave as
random components in their time series plot where there is a serial
correlation in these two plots, as shown by the Durbin-Watson test
of the serial correlation.
108
The first difference of the residuals is calculated.
From the
time series plot of these differences and plots against the fitted
response
variable,
we
note
that
the
differential
residuals
in
Fig(4-1) (of the models which fit number of accidents Y1 in Saudi
Arabia) behave as a random component more than the differential
residuals in Fig(4-2) (of the models which fit number of injuries Y2
in Saudi Arabia).
Plot of the differential residuals against its normal scores
reveals that the plotted points in Fig(4-1) are more likely to fall
on a straight line than the one in Fig(4-2), which indicates that
the differential residuals
Fig(4-2).
in Fig(4-1)
are more
random than
in
These two models are:
/'.
Y1
=
6748
=
7274
/'
Y2
0.0028 X2
+
+
0.0039
0.0315
+
X3
X2
Plots of models of the second group, in which we do not reject
Ho are given in Fig(4-3) to Fig(4-5).
Time series plot of
the
residuals
in these
three
figures
behave as a random components, but the residuals of Fig(4-5), which
belong to the model which fits the number of fatalities Y3 in Saudi
Arabia, are more random than the other two plots.
In this group
there is no serial correlation in the residuals.
The plotted
points
in
plot
of
the· residuals
against
the
corresponding fitted response variable for all the three plots do
not foliov any specific pattern and the plotted points fall in a
rectangular scatter diagram.
are normally distributed.
This indicates that these residuals
109
To check for the normality of residuals we examine the plot of
the residuals against its normal scores.
In this case the plotted
Our plo ts sugges t
points are nearly on a straight line.
this is
so.
Hence we conclude that the residuals in these three models are
normally distributed.
/'
Yl
5613
=
'"
Y2
8714
=
0.0054
+
26549
X2
0.0051
+
+
These models are:
0.0015
+
0.2946
X6
Xl
Xl - 0.0005
X2
+
0.0182
X6
Plots of models of the third group, the inconclusive test, are
given in Fig(4-6) to (4-8).
Again the serial correlation appears in
the residuals.
The time series plots of the residuals,
in all these plots,
are not randomly distributed but exhibit cyclic patterns, which is
quite clear in Fig (4-6).
The first order difference is used to remove these patterns.
Again, the time series plots of the differential residuals exhibit
cyclic patterns in all the plots.
The second order difference of the residuals is made to remove
these patterns.
The plot of the seco.nd order difference of the
residuals reveals that the cyclic patterns are still there except in
Fig (4-8),
which belongs to
the model which
fits
the number of
fatalities Y3 in Saudi Arabia.
The plot of
against
randomly
the
second
its normal scores
distributed.
We
order
difference
indicates
that
the
conclude
that
the
of
the
residuals
residuals
residuals
are
not
of
the
110
first and second models in Fig(4-6) and (4-7), (which belong to the
models which fit number of accidents Y1 and injuries Y2 in Saudi
Arabia) are not randomly distributed,
even after calculating the
second order difference.
I
But the residuals which belong to the model which fits
the
number of fatalities Y3 in Saudi Arabia behave as random components
after calculating their second order difference.
The plot of this
difference against the time sequence and against the fitted response
variable reveals that these points are randomly distributed.
The
plot of this difference against its normal scores is also supportive
of the argument.
The three models of this test are:
,...
Y1
=
=
7440 + 0.0050
X2 + 0.0494
X4 - 0.0398
4364
+
0.0412
X3
0.0211
X5
2025
+
0.0004
X1 + 0.0043
X3
+
X5
Hence, for Aitkin's adequate subset approach, we conclude that
the number of newly regis tered . vehicles
issued
driving
licences
(X3)
are
the
(X2)
most
and
the number of
frequent
predictor
variables in the models which fit the number of accidents, injuries
and fatalities in the different regions of Saudi Arabia, where, in
most
of
the
models,
X2 and X3
have
a
positive
effect
in
the
regression model.
The number of taxis (X6) has a. negative effect in all of the
regression models which fit the number of the injuries (Y2) in the
different regions of Saudi Arabia, except for the Riyadh and Dammam
regions, where it has a positive effect.
Th~
population size
(X1),
the
number
of
newly
registered
vehicles (X2), the number of issued driving licences (X3), and the
number of
transport
vehicles
(X5)
have an equal
effect
on
the
111
regression models which fit
the number of fatalities
(Y3) in the
different regions of Saudi Arabia.
4.9.2 BACKWARD ELIMINATION AND FORWARD SELECTION PROCEDURES:
In the backward elimination procedure, as described in section
(4.6), we first find the best regression model with 7 predictors,
then
with
6
predictors,
significance.
0.10.
under a
determined
level
of
The resulting models for selected regions are given
in Tables (4-8) to
0( =
etc.,
(4-10),
where we use a
level of significance
All these models, we note, consist of a big number of
predictor variables, which are not performing in searching for the
good
models.
elimination
All
the
procedure
models
are
which
highly
are
given
significant
by
at
the
0.01
backward
level
of
significance.
We note that the predictor variable X1,
contributes
in
fitting
the
number
of
the population size,
accidents,
injuries
and
fatali ties in all .the models of Tables (4-8) to (4-10).
For the forward selection procedure, we first find the best
regression model with 1 predictor, then with 2 predictors, ••• 9tC.,
under a determined level of significance,
~
=
0.10.
The resulting models are given in Table
models we note again that
(4-11).
the predictor variable X1
From these
is
the most
contributing variable among all the seven predictor variables.
Hence the predictor variable X1 fits the number of accidents ,
injuries and
fa tali ties
in Saudi
Arabia,
regions except for the models which fit
(Y3) in the Makkah region.
the
Riyadh
and
l~akh
the number of fatalities
We find that X5 (the number of transport
vehicles) is the most contribute predictor variable with positive
effect for Makksh region.
"
112
X5, also has a positive effect on the models which fit
the
number of accidents and injuries in the Makkah region.
If we look at the models of the backward elimination and the
forward selection procedures, we note that there are a few models
(four models) which are
common in both procedures.
These models
are:
For Saudi Arabia:
/'"
Y2 = -
19634
--- =
13
0.0039
Xl
4801 + 0.0008
Xl
+
+
0.0149
X3
0.0005
X2 + 0.0044
X3 + 0.0030· X5
X2
1:7
For the Riyadh region:
/'.
Y2
- 20511
0.0188
+
Xl - 0.0072
0.4954
+
For the Makkah region:
/'
Yl
=-
3150
+
0.0028
Comparison
Xl
+
between
0.0216
the
X4
+
models
0.0120
which
X5
are
given
by
Ai tkin' s .
adequate subset approach and by the forward selection and backward
elimination procedures, are made.
of
the
models
which
are
We can conclude that about 40%
selected
by
the
forward
selection
procedure are the same models which are given by Aitkin's adequate
subset approach with the same F and R2 values.
As
we
mentioned
earlier,
Xl
is
the
most
predictor variable for Saudi Arabia, the Riyadh and
to
the
models
fatalities
by
which
fit
the
using
the
backward'
selection procedures.
number
of
contributing
accidents,
elimination
regions
l~akh
and
injuries
the
and
forward
113
But for the same regions as given in Tables
(4-1)
to
(4-7)
we find that the predictor variables X1, X2, X3, X4 and X6 are of
equal
contribution
accidents,
in
injuries
the
and
models
which
fatalities
by
fit
using
the
number
Aitkin's
of
adequate
subset approach.
Attention is drawn to the fact that some shortcomings in the
available data prevent very satisfactory models being fitted.
4.9.3 POISSON REGRESSION:
As we mentioned earlier in Section 4.7,
model
in fitting
the
number
of
road
traffic
the use of Poisson
accidents
in Saudi
Arabia is not suitable by using the same regressor variables.
it is arguable that
with
the
given
So
this approach cannot sensibly go any further
data
as
indicated
by
the
log-likelihood
ratio
statistic which is used as an inference to measure the goodness of
fit.
Finally we still deal with linear regression models as given
in the previous sections.
4.9.4 THE USE OF DUMMY VARIABLES:
The
any
dummy variables
differences
fatalities
in
in
the
the
technique is
number
different
of
regions
used
to see if
accidents,
of
Saudi
there are
injuries
Arabia,
as
and
was
described in section (4.8).
For
Saudi
the
number
Arabia we
different
of
can say
regions,
and
accidents,
injuries
that
there
are
differences
region
has
a
each
and
fatalities
different
between
in
the
regression
model with a different set of parameters and coefficients as given
in the separate models.
114
For the Riyadh,
Makkah and Dammam regions,
the accumulated
number of newly registered vehicles (X2), has a negative effect in
all the separate regression models for YI,
population
licences
size
(X3)
(XI)
there
and
are
the
number
positive
of
effects
Y2 and Y3.
yearly
for
all
For the
issued driving
the
separate
regression models except for X3 in model (9).
For the other regions the effect of the predictor variables
is different in some regions than in others,
separated regression models.
as appears from the
115
fable(4-1)
fatalities
: The minimal adequate sets of the accidents,
in Saudi Arabia.
model
V1 =-325U8 + 0.0062
V1 = 6748 + 0.0028
Vl = 5613
0.0054
/141
f1 =
0.0044
Vl = 7440
0.0050
6079
0.0575
Y1 =
•
•
•
•
d. f.
Xl
X2
0.0315
X2 • 0.2946
X2
0.8395
X2 + 0.0494
X3 + 0.0181
•
•
X3
X6
X7
X4 - 0.0398 X5
X4 - 0.1544 X6
Y'L =-'L654!ol + 0;0051 Xl
V2 =
7274
0.0039 X2
Y2 :
4364
0.0412 X3
0.0211 X5
V2 = 5695 • 0.0450 X3 + 0.0174 X4
Y2 = 54tH + 0.0494 X3 - 0.2123 X6
•
•
V3
V3
t V3
t
Y3
'Y3
, Y3
I
Y3
I
V3
I
Y3
V3
Y3
I
•
•
I
:
==
=
====-
2025
540
594
9516
9829
8714
4034
: - 3667
=- 4502
570
=
=
604
No serial
•
+
+
•
+
+
+
•
+
•
•
•
0.0004
0.0067
0.0061
0.0016
0.0016
0.0015
0.0007
0.0007
0.0008
0.0002
0.0005
Xl
X3
X3
Xl
Xl
Xl
Xl
Xl
Xl
X2
X2
-
•
0.1977 X6
0.6939 X7
+ 0.0043 X3
•
•
-
+
+
•
+
+
0.0040
.0.0040
0.0007
0.0008
0.0005
0.0021
0.0026
0.0246
0.0048
0.0032
X4
X5
X2
X2
X2
X4
X5
X6
X3
X5
+ 0.0022 X4
+ 0.0022 X5
+ 0.0182 X6
•
+
•
0.0224
0.0282
0.0667
+ 0.1473
+ 0.0375
correlation appear in the model.
X6
X6
X7
X7
X6
R~
injuries and
.Rt
d
F
13
12
12
12
11
11
94.6
94.0
96.5
91. 4
93.2
91.3
94.1
93.7
95.9
90.0
91.4
89.0
0.79 225.9
0.68 105.4
1.84 163.3
0.76
63.8
1.03 50.3
38.6
0.76
13
13
12
11
11
96.5
93.3
93.0
95.2
93.5
96.2
92.7
92.0
93.9
91. 7
1. 43 359.6
0.74 179.9
0.79
79.3
1. 49
72.9
1. 33 52.6
12
12
12
11
11
11
11
11
11
11
11
93.2
94.0
97.0
94.1
94.3
93.5
94.2
95.5
93.3
93.8
94.3
92.0
93.0
96.5
92.5
92.8
91.7
92.6
94.3
91.5
92.1
92.7
0.96 81.8
1. 41
93.6
1. 72 193.5
1.56
58.1
1.44 61. 1
1. 49
52.7
59.1
1. 52
1. 75
78.6
1. 73
51. 1
1.83 55.1
1. tiO 60.5
116
Table(4-2) : The minimal adequate sets or the accidents,
tatalities in Riyadh region.
model
d. f.
R""
injuries and
R~
d
F
I
Y1
=-;;i4578 + 0.0327 Xl
-0.0092 X2
VI =- 7711 + 0.0010 Xl +0.0216 X3
VI =- 8,"52 + 0.0116 Xl +0.0191 X4
•
*
•
Yl
Y1
=-14747 t
2874 +
VI = 28n +
VI = 3432 +
VI = 3577 +
=
0.0149 Xl +0.3592
0.0069 X2 +0.4183
0.0068 X2 +0.0003
0.0567 X3 +0.0204
0.0020 X2 +0.0362
+ 0.6344 X"!
Y2 =- 3402 + 0.0045 Xl
•
'1'2 =
Y2 =
Y2 =
V2 =
Y2 =
Y2 =
Y2 =
•
•
•
•
•
Y3
'1"3
Y3
'(3
'1"3
'(3
Y3
==
=
=
=
=
=
1882
1575
1932
1955
1839
1"H8
1668
314
176
155
96
130
142
158
No serial
+ 0.0016 X2
X6
X6
X3 + 0.4178 X6
X5 + 0.8768 X7
X3 ..- 0.0184 X4
..- 0.0111 X4
+ 0.0023 X2 + 0.1297
+ 0.0039
+ 0.0014 X2 + 0.0044
+ 0.0009 X2 ..- 0.0067
+ 0.0148 X3 + 0.0112
+ 0.0175 X3 - 0.0090
+ 0.0395 X6
+ 0.0012 X2
0.0004
0.0001
0.0001
0.0002
+ 0.0019
+ 0.0020
+ 0.0019
+
+
+
+
Xl
X2
X2
X2
X3
X3
X3
X6
X3
X5
X3
X5
X4
+ 0.4129 X7
+ 0.2705 X7
+ 0.0110 X5
..- 0.3372 X7
66.1
64.5
84.5
90.9
86.8
86.8
84.9
37.1
32.6
32.6
59.6
39.6
24.2
20.6
10 85.3 79.4 0.93
14.5
1.07
1. 22
1.54
0.82
0.88
1.26
1. 18
35.2
13.6
15.0
8.0
8.2
8.2
8.6
10 67.7 54.7 1.63
5.2
73.1
69.4
71.4
66.6
11 69.1
11 69.1
11 70.0
13
12
12
11
83.7
61.9
81.9
89.3
84.6
83.2
80.8
70.9
64.3
66.6
60.0
60.7
60.7
61. 8
+ 0.0226 X5
+ 0.0012 X3
+ 0.0018 X4
+ 0.02:.n X6
+ 0.0022 X4
+ 0.0014 X5
+ 0.0418 X7
correlation appear
1.22
0.89
0.85
1.92
1.60
1. 60
1.00
12
12
12
12
12
11
11
in the model.
13
12
12
12
12
12
12
60.0
57.8
66.8
75.5
75.6
69.1
61.4
56.9
50.7
61.3
71. 5
71.5
64.0
55.0
1.06
0.96
1. 01
2.24
1. 41
1. 34
1. 32
19.5
8.2
12.1
18.5
18.6
13.4
9.6
117
Table(4-3) : The minimal adequate sets of the accidents,
tatalities in Makkah region.
model
•
•
•
•
•
•
•
Yl =
1634
Yl = -14537
Yl = - 4566
Y 1 = - 4258
Yl = - 7339
1567
Yl =
Yl =
143~
Y1 =
1582
Y1 =
1423
Yl =
2009
= =
=
=
=
•
Y2
Y2
•
•
•
•
'i2
Y2
Y2
Y2 =
•
Y3
=
8956
2597
2005
1980
2401
2857
•
•
•
•
: No serial
=
=
..
.
..
..
.
..
..
.
..
..
.
.
..
..
321
625
279
266 +
Y3
Y3
Y3
= -
...
..
..
..
d. f.
injuries and
...
R1
Ra
0.0457
0.0100
0.0037
0.0034
0.0055
0.0019
0.0019
0.0033
0.0322
0.0620
X5
13
Xl - 0.0028 X2
12
Xl
0.0228 X3
12
Xl
0.0305 X4
12
Xl
0.1102 X6
12
X2
0.0293 X3
12
X2
0.0332 X4
12
X2
0.1661 X6
12
X3 + 0.0382 X4 - 0.1669 X6 11
X4 - 0.1816 X6 - 0.2371 X7 11
87.1
83.9
85.6
94.4
85.9
84.7
94.3
85.8
87.4
82.9
86.1
81. 2
83.2
93.5
83.5
82.2
93.3
83.4
84.0
78.2
0.0069
0.0039
0.0591
0.0443
0.0887
0.0777
Xl
13 87.3
X2
13 85.4
X5
13 84.0
X3
0.0446 X4 - 0.2851 X6 11 83.0
X3 - 0.2688 X6 - 0.5254 X7 11 78.5
X4 - 0.3081 X6 - 0.4176 X7 11 79.1
0.0067
0.0006
0.0003
0.0059
X5
Xl + 0.0069 X4
X2 + 0.0073 X4
X3
0.0075 X4 - 0.0248 X6
90.8
94.2
94.0
89.9
..
...
...
..
..
..
correlation appear
in the model.
13
12
12
11
d
1. 46
F
1. 50
2.13
1. 21
1. 45
2.20
1. 07
1.84
1. 88
87.6
31. :£
35.5
101. 5
36.4
33.3
98.7
36.2
25.5
17.8
86.4
84.3
82.8
78.4
72.6
73.4
1. 32
1.03
1. 22
1. 77
1. 79
1. 70
89.6
76.1
68.2
17.9
13.4
13.9
90.1
93.3
93.0
87.1
1. 30 127.9
2.43
97.9
2.52
93.9
2.56
32.6
1. 24
118
'.
Table!4-41
fatalities
: The minimal adequate sets of the accidents,
in Dammam reglon.
model
•
•
•
•
•
•
Yl = Yl =
Yl =
Yl =
Yl =
•
•
VI =
.
•
•
"
"
•
•
•
•
•
•
•
•
Y1
VI
=
1490
446
418
674
647
- 7433
+
+
+
+
•
+
-
=
6494
•
537 -
0.0025
0.0014
0.0118
0.0166
0.020<:
0.0105
0.0190
0.0093
0.0203
0.0268
0.7167
Xl
X2
X3
X3
X3
Xl
X4
Xl
X5
X4
X7
Y2 = - 2138 + 0.0035 Xl
Y2 =
600 + 0.0020 X2
Y2 =
946 + 0.0249 X3
- 915 + 0.0274 X3
Y2 =
Y2 =
627 + 0.0173 X3
Y2 = - 2814 + 0.0046 Xl
Y2 = -10405 + 0.0147 Xl
Y2 =
1278 - 0.0006 Xl
Y2 =
819 - 0.0005 X2
V2 =
753 - 0.0483 X4
- 1.3234 X7
•
Y3 =
Y3 = Y3 = Y3 = Y::l =
Y::l =
Y3 = Y3 =
Y::l =
•
: No serial
•
d. f.
169
1934
456
347
148
131
242
140
160
•
0.0036
0.0027
0.0008
0.0006
0.0004
0.0003
0.0006
- 0.0064
- 0.0066
+
+
+
+
+
+
X3
Xl
Xl
Xl
X2
X2
Xl
X4
X4
0.3983
0.4448
0.3128
- 0.0180
- 0.0218
- 0.0053
+
+
+
X6
X6
X6
X4 + 0.6128 X7
X5 + 0.6346 X7
X2 + 0.0145 X3
- 0.0046 X2
+
0.0170 X3
+ 0.0462 X5
+
0.5665 X6
+ 0.3596 X6
+ 0.4268 X6
+
+
+
+
0.3273
0.0026
0.0055
0.0199
0.0216
0.0773
X6
X2
X2
X3
X3
X5
+ 0.0179 X3
+
d
10 87.4 82.3 2.93
17.3
10 84.7 78.6 3.01
13.9
10 82.9 76.0 1. 78
12. 1
11
11
11
77.3
78.8
80.8
78.8
80.2
.69.9
70.2
67.1
67.8
73.5
75.3
77.6
75.3
76.9
61. 8
62.1
58.1
59.0
1.80
1.96
2.14
2.39
1. 73
1. 39
1.94
1. 46
1. 50
+
+
+
+
+
+
correlation appear
20.4
22.3
25.3
22.3
24.3
8.5
8.7
7.5
7.7
0.6602 X6
10 78.9 70.4 2.45
0.0011
0.0426
0.1713
0.0554
0.2126
0.0041
0.0113
0.009!>
F
52.0
54.3
47.5
13.4
15.9
- 0.0199 X4 11
+ 0.1143 X7
+ 0.0356 X7
R~
12 89.7 87.9 1.94
12 90.1 88.4 2.03
12 88.8 86.9 1. 43
11 78.6 72.7 2.07
11 81.3 76.1 2.23
12
12
12
12
12
- 0.0193 X4
- 0.0202 X5
rf
injuries and
13
X2
12
X6
12
X7
12
X6
12
X7
12
X4 + 0.0048 X5 11
X5 + 0.0505 X6 11
X5 + 0.1566 X7 11
in the model.
75.0
85.1
80.7
85.0
74.7
82.2
71.9
73.9
70.7
73.1
82.6
77.5
82.5
70.5
19.2
64.2
66.7
62.7
1. 75
1. 66
1. 45
1. 63
1.25
1.69
0.82
1.1'9
1.77
9.3
39.1
34.3
25.1
34.0
17.7
27.7
9.4
10.4
8.8
119
1'able(4-5)
fatalities
: The minimal adequate sets of
in North reg ion.
the accfdents,
model
•
•
•
•
it
•
it
it
•
d. f.
13 95.6 95.2 1. 34 280.8
Y2 =
699 + 0.0085 X2
13 88.9 88.0 1.80 103.8
Y3 =
Y3 =
Y3 =
Y3 Y3 =
Y3 =
Y3 =
110
250
291
114
16
93
51
+ 0.0013 X2 + 0.0029 X3
0.0001 Xl + 0.0014 X2 +
- 0.0002 Xl + 0.0020 X2 +
0.0013 X2 - 0.0021 X4 +
+ 0.0014 X2 + 0.0065 X5 +
+ 0.0013 X2
0.0061 X5
+ 0.0124 X3 + 0.0281 X4 0.7271 X7
+ 0.0721 X6
-
..
..
-
..
0.0078
0.0866
0.0089
0.0570
0.1390
0.0231
: The minimal aaequate sets of
in QUBseem region.
12
11
11
11
11
11
the accidents,
d. f.
Yl = - 2096 + 0.0043 Xl
Yl =
252
0.0045 X2
342 + 0.0634 X3 - 0.4746 X6
Yi =
..
•
•
Y'L
Y2
Y'L
=
=
=
- 2909
.
.
..
.
..
Y3
Y3
Y3
Y3
Y3
Y3
Y3
=
-
94.6
93.7
93.4
93.3
95.0
93.9
1. 74 123.9
1.93 10.9
1. 20 67.2
2.07
66.1
2.76
87.1
2.49
72.2
33.0
_.
=
=
=
=
=
+ 0.0059 Xl
329
0.0063 X2
523 + 0.0831 X3 - 0.7575 X6
.
..
544
0.0011 Xi
70
0.0012 X2
52
0.0171 X3
115 - 0.0082 X4
0.0318 X5
104 + 0.0103 X4 - 0.1102 X6
113 + 0.0183 X5 - 0.0678 X6
0.9546 X7
93
0.0133 X5
..
.
..
..
..
: No serial
R1
injuries ana
R~
d
F
13 88.2 87.2 1. 81
13 88.3 87.4 1.98
12 70.5 65.6 1. 49
96.7
91.6
14.3
13 85.8 84.1 1.03
13 86.9 85.9 1.23
12 69.5 64.4 1. 58
78.6
86.3
13.1
13
13
13
12
12
12
12
.
..
95.4
95.1
94.8
94.7
96.0
95.2
09 94.8 91.9 2.56
model
it
X5
X6
X5
X6
X7
X5
No serial correlation appear in the mode 1.
fatalities
•
F
d
475 + 0.0089 X2
'I',,0Ie(4-£;1
it
...
R",
Yl =
:
it
R"
injuries and
correlation appear in the model.
"
88.6
86.9
62.6
62.7
62. <\
66.0
2.26 101.0
2.02 85.9
1.07
21.7
10.1
1.60
10.0
56.'L 1. 78
60.3 1. 80
11.6
62.4 56.1 1. 77
1U.0
87.7
85.8
59.7
56'.5
120
Tacie(4-7)
:
iata..! i t les
in South r"egio_n ..
The minimal adequate sets of the atcioeMts,
model
•
•
•
•
*
•
•
•
•
Yl
'il
Yl
'il
'il
'i1
'il
'il
'i2
'i2
'i2
'i2
'l2
'i2
'l2
'l2
'l2
•
•
•
I
•
=
=
=
~
=
~
=
=
d. f.
..
..
.
..
0.0123 X2
5
2424
0.0020 Xl
0.0030 Xl
- 3961
2176
0.0015 Xl
3U6 + 0.0321 X2 35
0.1300 X3 +
29 + 0.1280 X3
196 + O. 1453 X3 -
..
..
-
..
..
..
..
0.0686
0.0269
0.0262
0.1183
0.1057
0.0440
0.0529
0.9792
X3
12
X2
0.1282 X4 11
X2 - 0.1843 X5 11
X3
6.0304 X7 11
X4
0.4843 X6 11
X4 - 6.3294 X7 11
X5 - 6.1406 X7 11
X6 - 4.5733 X7 11
X2
X3
X3
X5
X5
X4
..
= ===
=
=-
..
.
..
0.0074
0.0649
0.0634
0.0353
0.0537
0.0902
=
..
0.0972 X4 - 0.5180 X6
..
0.0915 X3 - 1. 0747 X6
=
=
6724 + 0.0051 Xl +
1803
0.0017 Xl
2712 + 0.0022 Xl +
576 + 0.0837 X3
375
0.0866 X3 +
9250
0.0070 Xl - 0.6l6B X6
0.0069 Xl - 9134
- 0.7691 X7
621
0.0020 X2 +
- 2.2823 X7
555
0.0941 X3
- 2.8748 Xl
..
..
.
'i3 =
'l3 = 'l3 =
'l3 =
'l3 =
'l3 =
-
383
1852
1765
54
94
74
..
-
0.1013
1.1365
4.1387
1.3323
4.6530
0.0156
+
+
+
+
0.0014
0.0013
0.0142
0.016l
0.0181
11
11
11
11
11
R'
RA
97.4
97.1
97.0
97.2
96.7
98.0
97.8
96.9
97.0
96.3
96.2
96.5
95.8
97.4
97.2
96.0
1. 42
3.08
2.05
1. 13
2.53
1. 31
1. 41
1.88
95.7
96.6
97.0
95.7
95.7
94.5
95.7
96.2
94.6
94.5
2.62 81.4
1.60 105.2
1.30 118.9
1. 34
81.9
1.00 80.7
d
F
226.5
122.9
119.8
128.6
107.9
176.2
160.1
113.7
10 95.4 93.5 2.15
51.2
10 95.4 93.6 2.22
51.8
10 95.3 93.5 0.81
51. 2
10 95.9 94.2 0.91
57.8
0.0218 X4 - 0.9325 X6
+ 0.0003 Xl
.
X4
X6
X7
X6
X7
X5
Injuries and
+ 0.0106 X3
Xl - 0.0250 X4
Xl - 0.0258 X5
X3 + 0.0066 X5
X3 - 0.1582 X6
X3 - 0.6335 X7
No serial correlation appear in tt.e mode I .
80.6
86.2
7B.9
78.8
82.5 79.6
12 82.6 79.7
12
12
12
12
12
83.4
88.1
81.9
81.8
1. 35
2.49
1. 82
1. 16
1. 09
0.84
30.1
44.6
27.1
26.9
28.3
28.6
121
~able
(4-6)
The best subset of the accidents, injuries and fatalities
in Saudi Arabia by using the backward el imination procedure.
d. f.
R"
-54065 + 0.0092 Xl - 0.0025 X2 + 0.0091 X3
+ 0.OZ23 X4 - 0.0233 X5 + 0.0497 X6
- 0.2065 Xl
7
96.2
54.1
=
-57658 + 0.0098 Xl - 0.0032 X2 + 0.0120 X3
+ 0.0274 X4 - 0.0275 X5 - 0.2035 X7
6
96.2
70.9
=
-531ZY + U.Oo!H Xl - 0.0026 X2 + 0.0122 X3
+ 0.0270 X4 - 0.0284 X5
9
96.1
93.6
=
-;<:Y43U + 0.0055 Xl
- 0.0300 X5
10
97.7
106.2
'1
=
-37746 + 0.0066 Xl
0.0393 X5
11
97.0
118.0
,'2
=
-26133 + 0.0049 Xl
0.0011 X2 + 0.0157 X3
- 0.0077 X4 + 0.0141 X5 + 0.0171 X6
- 0.2736 X7
7
96.4
62.2
=
-27359 + 0.0051 Xl - 0.0014 X2 + 0.0167 X3
- 0.0059 X4 + 0.0127 X5 - 0.2726 X7
8
98.4
82.6
=
-26964 + 0.0050 Xl - 0.0012 X2 + 0.0157 X3
+ 0.0078 X5 - 0.2846 X7
9
98.4
107.4
=
-15882 + 0.0033 Xl + 0.0169 X3 + 0.0077 X5
- 0.1417 X7
10
96.3
140.6
(2
=
-16262 + 0.0033 Xl + 0.0165 X3 + 0.0066 X5
11
98.2
201.0
Y2
=
-lY634
12
97.8
267.3
Y3
=
- 5Z8Z
7
98.6
68.5
0.0291 X7
8
98.5
90.1
- 4999 + 0.0009 Xl - 0.0005 X2 + 0.0047 X3
- 0.0018 X4 + 0.0044 X5
9
98.5
117.4
10
98.3
143.0
model
1
1
1
1
(2
(2
(2
=
Y3
Y3
=
=
=
..
0.0148 X3 + 0.0314 X4
0.0401 X4
-
-
.
0.0039 Xl + 0.0149 X3
+ 0.0009 Xl - 0.0005 X2 + 0.0044 X3
- 0.0022 X4 + 0.0050 X5 + 0.0051 X6
-
Y3
.
F
0.0294 X7
- 5646 + 0.0010 Xl - 0.0006 X2
- 0.0017 X4 + 0.0046 X5
- 4801
+ 0.0008 Xl
+ 0.0030 X5
- 0.0005 X2
+ 0.0047 X3
-
+
0.0044 X3
lA I I varlabteg in the model are 9ignificant at the 0.1000 I eve I.
122
ble(4- 9
)
: The best subset of the accidents, injuries and fatalities
in Hiyadh region by using the backward el iaaination procedure.
d. f.
Rl.
0.0410 Xl - 0.0190 X2 + 0.0550 X3
0.0270 X4 - 0.0055 X5 - 0.2503 X6
1.2349 X7
7
96.7
29.8
-44686 + 0.0407 Xl - 0.0192 X2 + 0.0583 X3
0.02.14 X4 - 0.2.475 X6 + 1.2698 X7
8
96.7
39.3
-37131::1 + 0.034U Xl - 0.0136 X2 + 0.0377 X3
+ u.0090 X4 + 1.0568 X7
9
96.1
44.2
-382i:l2 + 0.0351 Xl - 0.0141 X2 + 0.0377 X3
+ 1.2.816 X7
10
95.7
55.9
-23098 + 0.0210 Xl - 0.0096 X2 + 0.0133 X3
+ 0.0061 X4 + 0.0021 X5 - 0.0997 X6
+ 0.5549 X7
7
93.4
14.1
-23202 + 0.0211 Xl - 0.0095 X2 + 0.0121 X3
+ 0.0082 X4 - 0.1008 X6 + 0.5415 X7
8
93.3
18.6
-20129 + 0.0184 Xl - 0.0072 X2 + 0.0037 X3
+ 0.0034 X4 + 0.4548 X7
9
92.6
22.5
10
92.3
29.8
11
91.8
41.2
1832 + 0.0017 Xl - 0.0007 X2 + 0.0010 X3
+ 0.0040 X4 - 0.0018 X5 - 0.0077 X6
+ 0.0002 X7
7
90.9
10.0
11::131 + 0.001"1 Xl - 0.0007 X2 + 0.0010 X3
+ 0.0040 X4 - 0.0018 X5 - 0.0077 X6
8
90.9
13.3
1b15 + 0.0015 Xl
0.0005 X2 + 0.0005 X3
+ 0.0034 X4 - 0.0017 X5
9
90.4
17.0
10
90.1
22.7
model
n
=
•
-49~ti
•
•
H
,{1
V1
V2
"12
Y2
=
=
=
=
=
=
•
-
=
-20541 + 0.0187 Xl
0.5350 X7
¥2
=
-20511 + 0.0188 Xl - 0.0072 X2 + 0.4954 X7
Y3
= -
1(2.
,{3
Y3
Y3
•
= = = -
1051
•
0.0015 Xl
- 0.OU22 X5
A 1 I varlables
-
in the model
F
0.0074 X2 + 0.0037 X3
0.0005 X2 + 0.0039 X4
are Slgnificant at the 0.1000 I eve 1.
123
: The best subset of the accidents, injuries and fatalities
in l1akkah region by using the backward elimination procedure.
,bleI4-10)
d. t.
Ra
7
96.4
27.0
8
96.4
35.7
9
96.1
44.4
- 0.1839 X7
10
96.0
60.4
+ U.0028
11
95.2
73.2
12
94.4
101.5
7
96.4
26.8
mOdel
'1
=
- 1622
+ 0.0019 Xl
+ U.0174 X4
+ 0.0009 X2 - 0.0150 X3
+ 0.0191 X5 + 0.0672 X6
- 0.1023 X7
f1
=
(1 =
-
3908 + 0.0033 Xl - 0.0126 X3 + 0.0179 X4
+ 0.0186 X5 + 0.0613 X6 - 0.1359 X7
- 2("13
+ 0.0026 Xl
+ 0.0240 X6
( 1 = - 2012 +
-
+ 0.0165
X4 + 0.0176 X5
- O. 1811 X7
Xl + 0.0199 X4 + 0.0156 X5
0.U2~
Xl + 0.0216 X4 + 0.0120 X5
r1
=
i1
= - 4258 + 0.0034 Xl + 0.0305 X4
1'2 =
Y2 =
:H~O
558 + 0.0009 Xl + 0.0030 X2 - 0.0343 X3
+ 0.0133 X4 + 0.0279 X5 + 0.1535 X6
- 0.1263 X7
•
0.0035 X2 - 0.0353 X3 + 0.0130 X4
0.0283 X5 + 0.1684 X6 - 0.1073 X7
8
96.4
35.7
•
0.0038 X2 - 0.0407 X3 + 0.0136 X4
X5 + O. 1924 X6
9
96.3
46.7
1969 + 0.0038 X2 - 0.0396 X3 + 0.0360 X5
0.2330 X6
10
96.0
59.3
0.0003 Xl - 0.0001 X2 - 0.0007 X3
0.0023 X4 + 0.0052 X~
+ 0.0152 X6
0.0332 X7
7
97.7
41.6
::136 + 0.0004 Xl - 0.0006 X3 + 0.0024 X4
+ 0.0052 X5 + 0.0138 X6
0.0351 X7
8
97.7
55.7
262 + 0.0003 Xl + 0.0023 'X4 + 0.0051 X5
+ 0.0120 X6 - 0.0372 X7
9
97.6
74.6
275 + 0.0003 Xl + 0.0067 X5 + 0.0193 X6
- 0.0390 X7
10
97.2
86.0
2046
+
Y2 =
1980
+ 0.0271
Y2 =
13 =
•
,,10
+
+
-
Y3 =
'1'3 =
1'3 =
All
F
-
vCJ.I'Jables
1 "
the DIode I are significant at the 0.1000 I eve I.
124
'.
,le(4-11
) :
The besl subset of the accidents., injuries and fatalities
by using the forward selection procedure.
model
0"
d. f.
R20
F
Saudi Arabia:-
1
1
=
-32508 + 0.0062 Xl
-37447 + 0.0066 Xl + 0.1925 X6
13
12
94.6
97.6
225.9
239.7
2
=
-26549 + 0.0051 Xl
-19034 + 0.0039 Xl + 0.0149 X3
13
12
96.5
97.8
359.6
267.3
13
12
11
88.9
93.2
97.4
104.5
81.8
136.9
10
98.3
142.9
-14i4i"
-lU818 + 0.0128 Xl
+ U.U149 Xl + 0.3592 X6
13
12
82.1
90.9
59.7
59.6
- 3402 + U.0045 Xl
-le5tl2 + U.0113 Xl - 0.0059 X2
-20511 + 0.0188 Xl - 0.0072 X2 + 0.4954 X7
13
12
11
73.0
84.4
91.8
35.2
32.4
41.2
13
12
60.0
79.9
19.5
23.9
1634 + 0.0451 X5
2336
0.0024 Xl + 0.0281 X5
310u + 0.0028 Xl + 0.0216 X4 + 0.0120 X5
13
12
11
87.1
92.6
95.2
87.6
75.1
73.2
13
12
11
87.3
93.4
95.1
89.6
84.6
71.0
13
12
11
90.8
93.2
95.8
127.9
82.9
83.3
2
3
3
3
::I
=
=
= = -
=
=
400U
2020
30"
- 4tlUl
+ 0.0008 Xl
+ U.0004 Xl
0.0043 X3
+ 0.0001 Xl + 0.0051 X3 + 0.0034 X5
+ u.OOOe Xl - 0.0005 X2 + 0.0044 X3
+ 0.0030 X5
+
or I-Ilyadto region: -
~
1
1
=
=
",
=
2
.~
3
'3
=
=
=
=
;:114 + 0.0004 Xl
540 + 0.0005 Xl + 0.0207 X6
lr Makkah
,1
:'1
r1
=
= = -
(2
= = -
re:.~ion-
•
12
=
13956 + U.0069 Xl
48u3 + 0.0041 Xl + 0.0289 X5
- 3894 + 0.0037 Xl + 0.0334 X5 - 0.3515 X7
t3
t;:l
=
=
=
321 + 0.0081 X5
202 + 0.U039 X3 + 0.0067 X5
301 + 0.U040 X3 + 0.0069 X5 - 0.0592 X7
(2-
t3
1110 olher var iab 1.es
the mode I •
.. et the 0.1000 significance level
for entry into
125
Table ( 4 -12)
Data set used lor the duaay variables technique.
"
year Y1
1971
1912
1913
1974
1975
1976
1911
1978
1919
1980
1961
1962
1983
1984
1985
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1963
1984
1985
1971
1972
1973
1974
1975
1976
1971
1978
1979
1980
1981
1982
1983
1984
1985
01524
03425
05469
05694
01266
08167
08698
08327
07215
08513
07905
09868
10206
11932
11613
01210
01556
02017
02264
02860
03624
03421
04407
04486
04561
04748
05426
06320
05953
00513
00455
00872
00841
01184
01368
01386
01292
01905
01805
01156
00976
01130
01183
01419
02396
Y2 Y3
1051
1562
2080
1111
3051
3660
3454
3498
3297
4266
3917
4096
3644
4553
4090
1761
1691
2521
3084
3676
4364
3637
5231
5924
5665
5637
7033
8420
7514
6350
0562
1127
1091
1453
1650
1065
1506
2187
2379
1501
1147
1604
1741
1987
2967
0082
0121
0152
0115
0301
0301
0444
0324
0285
0360
0299
0337
0375
0389
0398
0235
0326
0431
0403
0541
0728
0710
0902
0938
0699
0860
1122
1148
1047
0856
0091
0181
0179
0218
0324
0312
0307
0340
0449
0423
0361
0309
0365
0395
0533
XI
12
1167106 0061601
1201572 0079525
1236416 0105144
1212275 0139244
1309111 0189343
1349754 0270691
1390247 0415262
1431954 0494927
1474913 0515080
1519159 0655495
1586124 0773195
1636681 0985378
1669259 1160663
1743316 1270110
1799101 1297007
1609940 0031936
1656629 0045939
1104672 0066022
1754108 0108966
1804977 0161369
1660931 0255636
1916756 0355144
1974261 0493655
2033486 0599548
2033488 0136022
2094492 0664469
2186818 1039250
2256797 1194933
2329012 1312440
2403540 1400080
0764213 0023462
0786376 0029044
0809181 0036243
0832648 0051668
0856795 0074141
0683355 0113356
0909855 0144234
0937151 0199784
0965265 0259362
09942230344350
1038049 0419719
1071266 0505941
1105546 0608346
1140923 0656917
1171432 0697984
X3
010568
007786
023411
015703
023620
036471
059317
063548
055299
032952
011626
044655
075151
083245
130063
010400
010691
010153
018490
024643
026134
060162
060229
053568
048716
055161
051617
048425
061359
057434
006091
008671
007438
010092
031212
028147
022539
068021
070097
060145
036118
060115
063568
071785
078746
01 02 03 D4 05
1
1
1
1
1
1
1
.1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
'0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
I
1
I
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
I
1
1
I
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
year Yl
1971 00527
1972 00747
1973 00722
1974 00973
1975 00979
1976 01103
1971 01222
1978 01453
1919 01509
1980 01851
1981 01791
1982 02165
1983 ,02831
1984 02869
1985 03467
1971 00167
1912 00318
1973 00379
1974 00437
1975 00476
1976 00582
1977 00410
1978 00456
1979 00661
1960 00864
1961 00604
1982 01060
1983 01184
1984 01646
1965 01284
1971 00204
1972 00279
1973 00380
1974 00325
1975 00524
1916 00647
1977 00742
1978 01423
1979 01987
1980 01793
1981 01673
1982 01946
1983 02870
1964 03509
1985 05519
Y2 Y3
0683
1093
0915
1239
1013
1094
1452
1918
1919
1611
1924
2116
3361
2999
3432
0208
0487
0691
0736
0453
0621
0462
0636
0934
0973
1207
1457
1783
2174
1801
0298
0370
0543
0486
0689
0176
0902
1346
2379
2200
1840
2310
2506
2623
3990
0093
0113
0154
0166
0228
0281
0253
0349
0399
0425
0405
0443
0555
0480
0545
0033
0055
0064
0126
0097
0180
0134
0158
0253
0205
0207
0330
0345
0364
0297
0030
0032
0078
0066
0103
0173
0185
0305
0547
0399
0275
0412
0411
0363
0647
XI
12
0957919
0985699
1014285
1043700
1073961
1107260
1140471
1174892
1209932
1246229
1301164
1342801
1365769
1430114
1475877
0529181
0544528
0560319
0576569
0593269
06U661
0630031
0646932
0668400
0666452
0716799
0741801
0765537
0790035
0815316
1340318
1379188
1419185
1460342
1502692
1549275
1595753
1643625
1692933
1743721
1820585
1878844
1938965
2001012
2065044
0016068
0018651
0022371
0032984
0048721
0068651
0069582
0111397
0132889
0154811
0193368
0217332
0247164
0271426
0293905
0003680
0004987
0008701
0017624
0031201
0048566
0080785
0095192
0110539
0121060
0139501
0168335
0218275
0237615
0257286
0001795
0002039
0002493
0004334
0010566
0017543
0027346
0037954
0045698
0055721
0077011
0102575
0139628
0171363
0197983
13
002987
004069
004239
007134
001271
001666
00682II
037043
033345
040501
021378
018471
021822
023172
023198
000708
001184
001383
002693
005658
007065
010439
014833
011098
010283
005983
009569
014423
015422
010179
000768
000754
000579
003789
006348
008424
014511
013496
017746
013890
011692
014468
016642
022050
040713
01 02 03 D4 D5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0,
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0 0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0 0
0
0
0
0
0
0
0
0
126
Table'4-13):
ANOVA
table
for the
different
regions
of
Arabia by using the dummy variables technique.
Sum of squares
Source
M.S.
lhe response variable V1:-
For
1 ) Due to D and
x..
model
interactions
i.ne I uding
saturated
.
2)
uue to D and X
additive
with no interactions
a)
la D
uue to [)
adjusted
for X
t.d [)ue to X
Due to X adjusted
tor D
model
Due
3)
4)
d. t.
Saudi
Due
la
Residuals
Total
For
the
701168466
23
30485586
661445034
524796686
242788955
418656079
136648348
8
5
5
3
3
82680629
104959337
48557791
139552026
45549449
39723432
19557518
720725985
15
66
89
2648229
296326
255923598
23
11127113
243129981
156544972
24603275
218526706
86585009
8
5
5
3
3
30391248
31308994
4920655
72842235
28861670
12793617
13808412
269732010
15
66
89
852908
209218
5082283
23
220969
4728235
2871322
1341784
8
5
5
591029
574265
268357
3386450
18569.12
3
3
1128817
618971
354048
360363
5442646
15
66
89
interaction
response variable V2:-
Due to D and X. saturated
model including interactions
1)
2)
Due
model
a) Due
uue
b) Due
Due
to IJ and X.
additive
with no interactions
to D
la D adjusted
tor X.
to X
to X adjusted for
D
3) Due
to
4) Residuals
Tolal
For
interaction
the response variable V3:-
t l Due to D and X. saturated
model including interactions
2)
a)
Due to D and X.
additive
model with no interactions
Due to D
Due to D adjusted for
X
b) Due to X
Due to X.
adjusted for
3) uue la interaction
4 ) kesiduCils
Total
0
23603
5460
127
F1g14-l>
];..ests
the
of
residuals
the model
for
Vl= 6742 + 0.0028 X2 + 0.0315 X3.
3
•
7
2
o
•
2
-2000
MTB )
I11"B
dirt
•
3
5
o
•
c14 clS
> tSlpl ct5
3500·
2
3
1750+
6
•
O.
0
5
2
3
•
•
5
•
7
"TB
~
plot clS c13
1600+
o·
__ + _________ + _________ + _________ + _________ + _________
BOOO
12000
"TB > nsco clS cl6
16000
2.000
20000
,..
+.---Y1
28000
"TU) plot c15 clg
CI5
•
o·
•
-1600.
_______ .+ _________ + _________ • _________ • _________ + _____
-1."0
N'
•
_0.70
-0.00
0.70
1 .• 0
---CI6
128
Fig(4-2)
-
the
residuals
Tests
of
0.0039
X2.
Y 2= 7274 +
for
the .. ode I
•
R•• ld.
B
•
6
o
o·
•
3
3
2
7
•
2
•
-1750+
>
>
e" e"
e"
dirt
tspl
•
•
•
2
0
HTB
HTB
.0
2500+
B
C ••
2
•
3
1250+
•
•
3
2
•
•
o·
•
7
o
o
2
"TB) plot clS c13
•
6
•
•0
••
.2
••
C••
1200+
o·
-1200+
______ • _________ + _________ +. ________ + _________ + _______
9000
"TB
"TB
>
1200,?
1 SOOO
18000
21000
~
--+Ya
2.-000
nseD c15 c16
plot c15 c16
•
C ••
1200+
•
o.
________ • _________ • _________ + _________ + _________ • _____
-1.110
H_
•
-0.70
-0.00
0.70
LilO
---C16
129
Flg(4-3)
Tests
of
".
Yl= 5608
HTB > topl
the
reslduals
for
the model
0.0054
X2
+
0.295
X6.
+
c14
Res id.
5
o
1750+
6
3
0+
4
•
2
5
6
2
9
3
1
7
-1750+
1
-3500+
+-----+-----+-----+-----+-----+-----+-----+-----+
HTB >
plot
4
2
0
e
6
10
14
12
16
c14 c13
Resid.
0
2000+
0
0
0
0
0+
0
0
0
0
0
0
0
0
0
-2000.
0
-4000+
~
----+---------+---------+---------+---------+---------.--VI
6000
12000
16000
20000
24000
28000
"TB > ngeo c14 c15
HTB > plot c14 015
Resid.
o
2000+
o
o
0+
o
o
•
• •• •
0
•
•
•
-2000+
•
-4000+
--------+---------+---------+---------+---------+--------CI5
-1.40
-0.70
-0.00
0.70
1.40
130
Fig!4-4)
for
of
the
residuals
26549 + 0.0051 Xl.
~st
Y2=
"TB > lsp'
the lIodel
cl'"
2500*
9
Resid.
8
1250+
3
5
o
6
3
0+
4
"
2
2
7
5
-1250"
1
1
+-----+-----.-----+-----+-----+-----+-----+-----+
o
MTB
> plot
2
4
6
8
10
12
lA
16
cl4 c13
2400+
•
Resid.
•
1200+
•
•
0+
•
-1200+
•
•
•
•
•
•
•
•
•
•
-+
-+Y~
7000
10500
14000
17500
21000
"
24500
MTB > nSCD clA c15
HTU > plot clA c15
2400+
•
Resid.
•
1200+
•
•• •
0+
•
-1200+
•
• •
• •
•
•
•
________ + _________
-1.40
+ _________ + _________ + _________ + _____ ---C1S
-0.70
-0.00
0.70
1.40
131
Fig(4-5)
of
the
residuals
for
the
DIode I
8714 + 0.0015 Xl
0.0005 X2 + 0.0182 XS.
!!'sts
=
Y3
500+
9
Resid.
250+
3
2
a
v+
b
"
7
•
"
+-----+-----+-----+----+-----+..
o
2
4
b
8
10
HTB > plot
•
1
---+-----+-----+
1.
1b
c13
cl~
500+
•
+
+
•
•
1)+
•
•
•
•
•
+
-250+
+
•
•
----+---------+---------+---------+---------+---------+--Y$
bOO
12.(.1)
1800
2400
3000
3600
~
MTB ) nsco c14 cIS
MTB > plot c14 clS
•
Resid.
•
•
•
0+
+ +
-250 ....
+
•
•
•
•
•
•
•
--------+---------+---------+---------+---------+--------C15
-1.40
-0.70
-v.OO
1.40
0.7(1~
132
Fig(4-6)
for
the
residuals
".. Tests of
Yi = 7442 + O.OOSO X2 + 0.0494 X4
>
t'ITB
tspl
the .. ode I
0.0399 XS.
cl.
9
5
2000+
6
o
Resid.
B
5
3
0+
2
7
2
-2000+
3
1
-4000+
1
+-----+-----+-----+-----+-----+-----+-----+-----+
0
•
2
6
la
B
12
16
14
HTB > di tt cl' c15
HTB > tspl c15
C15
2
2000+
3
B
4
9
2
5
5
6
0+
o
-2000+
3
7
-4000+
"TB >
"TB >
+-----+-----+-----+-----+-----+-----+-----+-----+
4
0
2
dUf c15 c16
tspl
la
B
16
12
c16
6000.
2
C16
B
3000.
0+
5
3
9
6
5
o
7
-3000+
3
+-----+-----+-----+-----+-----+-----+-----+-----+
o
2
4
6
8
10
12
14
16
133
Cont·lnue.
Fig(4-6)
KTB
>
plot c16 c13
•
5000+
•
C16
•
2500.
•
0+
•
•
•
•
•
•
•
-2500+
•
•
-+
10500
N'
HT8
HTB
.
14000
17500
21000
24500
/'
+-)~
28000
2
> nsco c16 c17
> plot c16 c17
5000·
•
C16
•
•
2500+
0+
-2500+
-
.
•
•
• •
•
•
--------+---------+---------+---------+---------+--------Cl7
-1.20
N'
•
•
•
2
-0.60
-0.00
0.60
1.20
1.34
Fig(4-7l
~st
=
Y2
ttTa
)
the model
the
residuals
for
of
XS.
+
0.0412
X3
+
0.0211
4364
tapl
C14
Resid.
4
1500+
3
5
3
4
1
2
5
6
0+
2
9
0
1
-1500+
-3000+
e
7
+-----+-----+-----+-----+-----+-----+----- .. -----+
2
0
B
6
4
12
10
16
14
HTB > di tf cl. c15
HTB > tapl c15
C15
9
1
2
1750 ..
3
4
3
0+
0
B
4
5
5
6
2
-1750+
7
-3500+
tlTB
,.
+-----+-----+-----+-----+-----+-----+-----+-----+
o
12
10
B
6
4
2
16
> tspl c16
3500+
6
C16
3
9
1750+
1
0+
•
5
6
4
5
3
-1750+
o
7
2
+-----+-----+-----+-----+-----+-----+-----+-----+
o
2
4
6
8
10
12
14
16
N. = 2
134 1
Fig(4-7)
Continue.
HTB > plot c16 c13
•
C.6
•
•
2000+
•
•
0+
•
•
•
•
-2000"
•
•
•
•
--+---------+---------+---------+---------+---------+---y~
21000
18000
15000
12000
9000
6000
~
HTB > neeD c16 c17
HTB ) plot c16 017
C16
•
2000+
•
0+
•
-2000+
-
•
.
•
• • •
•
•
•
--------+---------+---------+---------+---------+--------C17
-1.20
-0.60
-0.00
0.60
1.20
135
Fig(4-B)
for
the model
the
residuals
of
2025 + 0.0004 Xl + 0.0043 X3.
Tests
Y3 =
Resid.
9
6
o
250.
2
3
5
1
o.
7
3
2
•
-250+
4
5
-500+
+-----+-----+-----+-----+-----+-----+-----+-----+
o
HTB
>
HT" >
2
4
10
B
6
12
16
14
dilt c14 c15
c15
t.spl
C15
9
300+
2
5
6
2
3
o·
•
3
o
B
5
1
7
-300+
•
..
-600+
+-----+-----+-----+-----+-----+-----+-----+-----+
0
HTB >
•
2
c16
tspl
6
12
10
B
16
700+
9
C16
2
5
3&0+
5
8
6
O·
3
1
4
3
-350+
4
7
0
..
+-----+-----+-----+-----+-----+-----+-----+-----+
0
N' = 2
2
4
6
8
10
12
16
135 i
Continue.
Fig(4-8)
HTB ) plot e16 e13
•
C.6
•
350+
•
0+
•
•
•
•
•
•
•
-350+
•
•
•
"
+---------+---------+---------+---------+---------+-----Y3
3000
3500
2000
2500
1000
1500
MT8 > nsco e16 c17
HTB > plot c16 c17
•
Clb
•
350+
•
•
o.
• •
-3: 0+
-
.
•
..
•
•
•
________ + _________ + _________ + _________ + _________ + _____ ---Cl7
-1.20
NI .. 2
-0.60
-0.00
0.60
1.20
136
Fig. (4-9): SAS program to fit the number of road traffic accidents
in Saudi Arabia by using a poisson regression modela
===================================================================
DATA NLIN;
INPUT YR Y1 Xl X2 X3;
CARDS;
1971 04147 6436283 0144768 031542
1972 07197 6622937 0180185 033357
1973 09808 6815004 0242974 047209
1974 10897 7012642 0355022 057901
1975 13475 7216010 0514361 098758
1976 15709 7439703 0774443 117911
19T1 15785 7662894 1112973 173788
1978 18051 7892780 1432909 257176
1979 17743 8129560 1723116 241153
1980 18758 8373444 2069479 206549
1981 17897 8742549 2467903 150178
1982 21597 9022312 3018811 198921
1983 24594 9311016 3569009 240031
1984 27348 9608970 3919871 283033
1985 29052 9916454 4144248 340333
PROC NLIN;
PARMs BO=126 Bl=1. 7 B2= 1.5 B3=1.9;
MODEL Y1= BO+(B1*Xl)+{B2*X2)+{B3*X3);
DER.BO=l;
DER.B1=Xl:
DER.B2=X2;
DER.B3=X3:
OUTPUT OUT=B P=YHAT R=YREsID;
00 1=1 TO 15;
D=2*Yl*LOG{Yl/YHAT);
ENO:
PROC PRINT: VAR D YHAT YRESID;
PROC MEANS; VAR D YHAT YREsID;
============================================================ PAGE 1===
\SAS\
NON-LINEAR LEAST SQUARES ITERATIVE PHASE
DEPENDENT VARIABLE: Y1
ITEHATION
BO
0
120.000000
-49274."1134"12
1
"
-49274.713460
~
METHOD: GAUSS-NEWTON
B1
1.7000000
0.0085089
0.0085089
B2
1.50000
-0.0030427
-0.0030427
B3
1.90000
0.0187456
0.0187456
RESIDUAL SS
4321950055584685
20400855. 69tlS5tl
20400855.698858
NU1'E: CONVERGENCE CRITERION MET.
============================================================ PAGE 2===
SAS
NUN-LINEAH LEAST SQUARES SUMMARY STATISTICS
DEPENDENT VARIABLE Yl
SUURCE
REGRESSION
RES1DUALS
UNCORRECTED TOTAL
DF
4
11
15
(CORRECTED TOTAL)
14
SUM OF SQUARES
4914655838.3
20400855.7
4935056694.0
700919076.9
MEAN SQUARE
1228663959.6
1854623.2
l
137
I
Fig.(4-9): continue
'.
PAkM~'rR
ASYMPTPTIC
STD. ERROR
~STIMAE
BO
BI
B2
83
-49274.71346
0.00851
-0.00304
0.01875
ASYMPTOTIC 95~
CONFIDENCE INTERVAL
LOWER
UPPER
-89628.331261
-8921.0956594
0.002385
0.0146331
-0.007424
0.0013385
0.0376869
-0.000196
18334.273405
0.002782
'0.001991
0.008606
ASSYMPTOTIC CORRELATION MATRIX OF THE PARAMETERS
BO
COkR
Bl
I.QOOO
-0.9992
0.9672
0.4624
BO
UI
H2
B:3
-0.9992
1.0000
-0.9652
-0.4851
B2
0.9672
-0.9652
1.0000
0.2693
B3
0.4624
-0.4851
0.2693
1.0000
;;;;;;;;;;;==;=;;=;;======;=;=====;==;=;;=;=========;;==;=;=;=
PAGE 3
SAS
OHS
D
YHAT
YRESID
1
-255.3.3
81. 4
1995.5
1016.3
2214.5
3882.1
-29.0
-584.1
-2'157.4
-1550.3
-4122.3
-875.1
20,,5.8
3047.8
213.4
5642.6
7156.4
8859.3
10400.5
12412.0
13883.1
15799.6
18345.4
191'i6.7
19549.4
20421.0
22039.0
23592.1
25865.8
288,'3.6
-1495.0
40.6
948.7
496.5
1063.0
1825.9
-14.6
-294.4
-1433.7
-791.4
-2524.0
-442.0
1001.9
1482.2
136.4
2
3
4
5
6
7
8
9
10
11
12
13
14
15
VARIABLE
lJ
'iH~SILJ
YHAT
N
15
15
15
MEAN
99.009
10801.1
O. 006E>',
STANDARD
DEVIATION
2365.4146
6971.9849
1207.1530
MINIMUM
VALUE
-4722.2368
5642.0000
-2524.0000
MAXIMUM
VALUE
3882.0559
28873.600
1825.9000
SUM
1485.14
252015.9
0.1
1
,
138
CHAPTER V
APPLICATIPN OF TIME SERIES MODELLING
5.1
INTRODUCTION:-
Selecting
appropriate models of time series for a given
set of data depends basically on many
of the series, type
factors
of the given data,
, such as
length
the dependency among the
variables, and the seasonality at specific time points.
To build a model, there is a plan which can be used for this
purpose.
This plan can be described in the following steps:
Model identification, model fitting and parameter estimation
and model checking or diagnostics.
In the next section we discuss the model building in detail.
Integrated autoregressive moving average
(ARIMA) process will be
described.
ARIMA modelling for
selected
data
from
the
road
traffic
accidents in Saudi Arabia are given in section 5.3.
Accidents, injuries and fatalities are the three variables
which have been used in time series modelling for three sets of
data, which are,
the daily data of Riyadh area, monthly . data of
Saudi Arabia and monthly data of Riyadh region.
Finally in section 5.4,
results and discussion about
chapter.are given in brief notes.
this
139
5.2
THEORETICAL CONSIDERATION:-
5.2.' MODEL BUILDING PROCEDURES:
There are three steps in the model building plan described in
the following, and these are used in the next section in finding
appropriate
,.
ARIMA models for the
data.
~iven
Model identification:
In this step we take the time series plot as an important
tool to recognise the change in behaviour of
wi th time, in other words,
series or not.
the
observations
to know if there is a trend in the
If so, we make a
transformation of the data to
remove· this trend before we do any kind of analysis, i.e.
to make
the time series stationary about the mean.
There
are
two
important
aids
in
time
series
analysis.
The
estimated autocorrelation function (acf) and the estimated partial
autocorrelation
function
correlations between the
(pacf).
They
are
observations within
measures
of
the series.
the
For
every ARIMA model there are a specific theoretical acf and pacf
associated with it, so the estimated acf and pecf can be used as a
guide to one or more ARIMA'models that seem to be appropriate.
choose the final model we proceed to
perhaps
return
to
the
first
the next
two
To
stages and
stage if the considered model
is
inadequate.
The acf can be defined
Y"
as
Y2'
... Yn and denoted by
fa" a given stationary data set
r
k
at time lag k =
"
2,
140
n·k
~
(Y -V)(Y
-V)
t
t+k
1= 1
k=I.2.3 •...
~
(Y
t= 1
( 1 )
_ Y )2
t
The pacf can be defined for a given stationary data set sequence
• • • ,Y n and denoted by
".
rp
11
~
r
at time lag k = 2. 3 •
1
r
-
k
~
k·1
.rk _ j
j=1 4>k_l.j
kk
1
-
",
~
k=2.3....
k·1
,."
j= 1
(2)
r.
I'k_l.j
J
where
...
...
...
...
<P kj
'" k - 1 • j
<Pk k
<Pk -I • k - j
k = 3 .4 •...
j=I.2" . ., k-I.
So we can compare the estimated acf and pacf with Borne common
theoretical acf' sand pacf' s. which are available in many text
books.
If we find a correspondence between the estimated and the
theoretical functions. we then select the process associated 'ofi th
the corresponding theoretical function as a tentative model for
the given data.
2.
Model Fitting:
The model which we select in the previous step is now fitted
to the given data to estimate its parameters.
The adequacy of the
model must be taken into account. In other words. if the estimated
parameters do not satisfy certain mathematical conditions such as
the
absolute
t-values
to
be
greater
proposed model will be rejected.
than
or
equal
two,
the
The methods of estimating model
parameters and adequacy of the model will be investigated when we
discuss the procedures of ARIMA models.
If our proposed model is
141
rejected, we must return to the first step and look for another
model.
3.
Model Diagnostics:
There
are
some
model
diagnostic checking made
on
the
residuals of the estimated model which help in determining whether
the estimated model is statistically adequate or not,
some
of
important
in
checking the model, where in the appropriate mode 1 they mus t
be
which are:The
residuals
of
randomly distributed.
the
estimated
model
are
The residuals can be calculated by first
finding the fitted model using the estimated parameters. Then
the residual et is given by e
= Yt
t
....
- Y •
t
If the ARIMA model is correct, then the residuals are iden-
tically distributed independent normal variates with zero mean and
varia.nce
=
a
2
• The residuals can be used in various ways to
check on the adequacy of the model.
The methods which have been
used in this chapter are:-
1)
Acf of the residuals,
where we can distinguish from the
correlogram (plot of residuals ~
versus the leg k) whether the
residuals are randomly distributed or not.
2)
Histogram of the
residuals,
which can verify whether
the
residuals are normally distributed or not, by looking to the shape
of the histogram.
3)
Normal scores of the residuals: We can check for the normali-
ty of the residuals more carefully by plotting the normal scores of
the residuals against the residuals itself, where the
ttb
.,
normal score
142
is (t-*)/(n+Y.) percentage point of the standard normal distribution,
where n is the time series lenght. Vii th normally distributed.
. -. data
,
a plot of the residuals against the corresponding normal scores should fall approximately or. a straight line.
4)
Plot of residuals against the fitted values: here we look for
patterns,
the
absence
of which
indicates
a
good
fit
for
the
model.
5)
Plot of the
adequate,
residuals against
the
time:
if
the model is
then the plot will be a rectangular scatter around a
zero horizontal level with no trends at all.
6)
Portmanteau test, Q*:
This tes t
looks to
the acf of
the
residuals as one group, not individually as before.
Let
be
~
the
acf
of
the
residuals
{et}
of
the
fitted
model, where
n-k
L
r
t=
k
I
••
t
t + k
k= 1,2,3, .....
n
( 3 )
.2
L
t=
1
•t
then calculate
m
Q• ..
n( n + 2 )
L.
k~l
r
2
/(n-k)
k
for SOme reasonably large m,
2
Q* ...... x
say 10.
(4 )
If the model is correct,
,where \' is the number of parameters estimated in the
m - v
ARIMA model.
If Q* is significantly large,
then another model
should be tried.
The Q* statistic is called the modified Box - Pierce statistic ...
143
A model which failS in these checks is
rejected and we return
again to the first step and look for another model until we find a
good model.
The good model has many characteristics such as
The
smallest
number
of
estimated
parameters
needed
to
adequately fit the given deta.
2 -
Stationarity, which implies in particular that the model has
a constant mean without any upward or downword trend in the time
series plo t
of
the data.
estimated acf dies quickly
In the acf of the series,
to
zero,
then the
if
series
the
is mean
stationary •
3 -
"qJ'.
4 -
The estimated coefficients of high quality such as I
t
I ;;;. 2, Md
and ,.
9'. are not too highly correlated with each other.
The residuals are randomly distributed or uncorrelated.
5.2.2 SOME ARIMA MODELS:
Let p, d, and q be
non-negative integers, where p is the order of
the auto regressive (AR) process, q the order of the moving average
(:.lA) process and d the number of times the series is differenced
in
order
to
become
stationary.
characterized in the following way:
So
any
ARIMA model
can
be
ARIMA (p, d, q)
If we have a seasonal time series we can deal with the sessonal·
ARIMA model which can be characterized as
ARIMA (p,d,q)s where p,d,
and q are defined as before and s denotes the seasonal period
which is equal to 12 in monthly data.,
equal to 7 in weekly data •
. •• etc •.
Multiplicative seasonal ARIMA model
is a
combination
of
144
seasonal and nonseasonal ARlHA models and denoted by ARIMA (p, d,
q) X (p, D, Q)s, where P, D, and Q are the orders of the seasonal
effect.
Before we introduce some ARlHA process, it is necessary to
gi ve a definition of the white noise process which is a sequence
of identically, independently distrbu~1
wi th a zero mean and variance denoted by
and autocorelation
The white
p =
noise
p
k
= 1 for k = 0 and
series
can be
Let
{at}
0 2
p
•=
k
0 for k
~
o.
AR( p) with order
considered as
o.
Moving average process
I
random variables
{Y t }
be
an
observed
MA(q):
time
series
and
{at} represent
the
white noise series, so we can define the moving average process of
order q as
y
Oq •
t
q
t -
( 5 )
Now we can describe the following process:
MA (1) Process:
oa
(6 )
t -
I
with mean, variance, covariance and autocorrelations
E(Yt) = 0
2
hence
P
=
I
respec ti vely.
'f I
'fo
= V(Y t ) =0.
'f
=
1
---=
1
2
+U )
2
Cov (Y t , Yt-l ) = _ 8 o
•
-0
I +0
(
2
and
p
= 0 ror k
k
>. 2
'"
145
"
The MA(l) model is in\Tertible if
MA(l)
can
be
inverted
into
18 1<
1, i.e. we say th!'t the
infinite
order
auto regressive
I~A
process.
(2) Process:
=
Y
t
a
t
-
0.
a
t-l
_
6
( 7 )
a
2t-2
The mean, variance, covariance and autocorrelations of the process
are given by
= V(Y t ) = (1
2
+
1
8
+
8
2
2
2
) aa
+ 8 8
)a 2
= Cov (Y t , Yt_l) = ( - 81
12
a
= Cov (Yt, Yt-2)=
8
a
2
2
a
hence
'Y
- 8 1 + 8 1 82
1
'Y
2
2
1+8 1 +6
2
o
and Pk = 0 for k ;;;. 3
respectively',
The MA(2) model is invertable if:
6
2
(8
1<
1
+ 8
2
<
1
• and
(8
2
-
8
1
)
<1
MA (q) Process:
'Y
o
= ( 1 + 8
2
1
+ ..... + 0
2
)a
2
a
lor k = I. 2.
for
k
>q
.
.
q
146
For the invertibility of.MA(q) where q
>
2, it is a necessary (but
not sufficient) condition that
(8
•
+8
2
+ ...... + 8 ) <
q
The invertibility conditions are necessary to
the estimates of
a's obtained at the estimatation state.
The lolA(q) process has the following properties:a)
Theoretical acf' s tail off toward zero after log q,
the MA
order of the process.
b)
Theoretical pacf's tail off toward zero with either some type
of exponential decay or a damped sign wave pattern.
The MA(1) process has the following properties:a)
Theoretical acf's have a negative spike at lag 1 if 8
>
0,
and have a positive spike at lag 1 i f 8 < 0, then it cuts off to
zerob)
Theoretical pacf's damp out exponentially on the negative
>
8 <
side i f 8
side if
° and
alternating in sign, starting on the 'positive
0.
Whereas for MA(2), we have the following properties:a)
Theoretical acf' s spikes at lags 1 and 2, then cuts off to
zero·
b)
Theoretical pacf depends on the signs and sizes of 8. and 82
where it'is exponential decay or a damped sine wave·
The following diagram illustrates
examples of theore-
tical acf and pacf for MA(1) and MA(2) process.
147
MA (I), 8
1.0
<0
1.0
pa"
P
k
4>kk
k
-1.0
-1.0
MA (I) 8 > 0
1.0
1.0
acl
pacf
Pk
k
-1.0
- 1.0
MA (2)
1.0
1.0
.. I
P
k
4>kk
pa"
k
k
-1.0
k
4>kk
-1.0
MA (2)
1.0
1.0
acl
P
pacl
k
k
-1.0
4>kk
k
- 1'.0
MA (2)
1.0
1.0
.. I
P
k
-1.0
pacl
k
4>U
-1.0
Examples of theoretical acf's and pacf's for MA(1) and MA(2) processes
.,
148
II
Autoregressive Process AR (p)
{Y
Let
t } be an observed time series and
noise series, then the AR(p) process is
{at}
V=</JV
.</Jv
+",+tj> V
+.
t
1
t-l
2
t-2
P t-p
t
a white
(8)
Now we can describe the following process:
AR (1) Process:-
vt
= tj>
vt
•
1
+ •
(9)
t
Assume that the' mean of the' series is subtracted out.... so
that
Yt has a zero mean.
Variance, covariances and autocorrelations
are given by
'Y
o
=
a
a
2
and
hence
...k
'P
for k = O. 1,
2.
. ..
respectively.
The AR(I) model is stationary if 191 < ) and the autocorrelation
function , is an exponentially decreasing curve as the number of
k
lags k increases.
AR (2) Process:
v=tj>V
t
I
t-l
+tj>v
2 t - 2
t
As before, Yt has a zero mean.
are given by
autocr~linB
(10)
+.
Variance, covariances, and
+
hence
'Yo
and
f:-. : 1~ -(-)
-tj>~
-:""':-)-2
a
2
•
}
149
Dividing by "I
o
Pk = '" 1Pk - 1 + '" 2 P
k-2
By using P0 =
and
!!.1
1
k = 1. 2. '"
= PI we can find that
+ ",2
1
"'2(1-"'2)
"'1
P =
for
and
P =
2
1-'"
2
1 - "'2 )
The stationary conditions for AR(2) are
I
"'2
I<
1. ( "'1 + "'2 )
<1
• and
("'2 -
"'1 )
<
1
AR(p) Process:
multiply the general AR model given in
Assuming stationary we
equation (8) by Yt-k and take the expectation. We
find that
k
By multiplYing equation(8)by Yt and
find that
"1="'''1
+"'2"1
by using P = "I
k
k
+ .... +"'1'+0
P
We
2
a
l'
0
0
l'
0
1
taking the expectation
I I
2 p
o
~
1 - '" 1 PI - "'2
2
a
P
2 - .•••• - '"p Pp
For the stationarity conditions of AR(p),
where p
>
2,
it is a
necessary (but not sufficient) condition, that
("'1
+ '" 2 +.. . . . .. + '"p
)
<
1
The stationary conditions are required for any AR model, because
we could not get useful estimates of the parameters of a process
if i t
is
not
stationary.
So we must have
a
fixed
mean
and
variance to the series to get a stationary model.
The AR process has the following properties:a) Theoretical
damped sign wave).
acf tails off toward zero (exponential decay or
150
b)
Theoretical pacf cuts off to zero after lag p.
To i!ssess
the possible magnitude of the pacf, Quenouille (1949) has shown
that,
under the hypothesis that an AR(p) model is correct,
the
estimated pacf at lags greater than p are approximately independently normally distributed with zero mean and variance l/n, where
n is the sample size.
Umi ts on
<I>
kk
Thus
+
2/ Vu
Can be used as
critical
for k >_p to test the hypothesis of an AR(p) model.
In particular for the AR(I) model we have,
a)
if
<I>
b)
Theoretical acf has an exponential decay on the positive side
<I>
<
> 0 and alternating in sign starting on the negative side if
O.
Theoretical pacf has a positive spike at lag 1 i f
<I>
>
J
and
negative spike i f <1>< O.
The AR(2) model has the following properties:-
a)
Theoretical acf depends on the signs and sizes of
<1>. and <1>2
where it is -exponential decay or a damped sign wave.
b)
Theoretical pacf has a spikes at lags 1 and 2, then cuts off
to zero.
The following diagram illustrates examples of theoretical acf and
pacf of AR(I) and AR(2) process.
15 1
AR(J) , ~
<0
1.0
1.0
pad
acf
P
k
k
k
<Pkk
-1.0
-1.0
AR (I) , ~
>0
1.0
1.0
p""f
P
k
~k
-1.0
·AR (2)
1.0
1.0
pacf
~kf-L.l
-1.0
k
- 1.0
AR (2)
1.0
1.0
pact
P
k
k
-1.0
~k
k
-1.0
AR (2)
1.0
1.0
oof
pad
k
-1.0
-1.0
Examples ot theoretical act's and pact's tor AR(1) and AR(2) processes
152
III
Autoregressive moving average process ARMA (p,q)
Let {Y t} be an observed time series and {: t} a white noise
series, ther,
the ARMA (p,q) is
y=rpy
I
t
+rpy
t-l
2
+ ..• +rpy
P
t-2
t-P
+.-Oa
1
t
t-l
-0.
2 t-2
- ... - 0 ,
q
t- q
( 11 )
Consider the following process:
ARMA (1,1) Process:y=rp
t
t-l
+a-O.
t
Multiply equation (12) by Y
t- k
r
o
r1
" rpr
1
( 12 )
t-l
and take the expectations, we have
+ (I - 0 (rp _ 0 ) ( 0
2
•
=
solving the first two equations yields
( 1 -
r0
+ 02 )
20 rp
0
_ rp2
2
a
.nd
rk =
(I - 0<1»
( <I> -
1 -
<I>
0 )
l-I 0 2
•
2
for
k ;;>1
for
1. ~
hence
P
k
=
(I-O<l»
1 -
( <I> -
2
20<1> + 0
0 )
rpk-I
I
153
The ARMA· (1 ,1) is a stationary process if I q, I
<
I
and I 9 I
<
I
The autocorrelation function decays exponentially as tCle lag k
increases.
For ARMA (p,q) it is necessary (but not sufficient) to check that
+
+
q,
2
+
__ ... , •
e2 + .. + eq) < 1
q, !
P
<
I
for
stationary
condition
and
for invertabili ty condition.
For ARMA processes:
a)
The theoretical acf tails off toward zero after the first(q-p)
lags with either exponential or damped sign wave.
b)
The theoretical pacf tails off towards zero after the first
(p-q) lags.
In general (p-q) is
usually not more than two in
ARMA models for nonseasonal time series.
The following diagram illustrates examples of theoretical acf and
pacf for ARMA (1,1) process, where both the acf and pacf tail off
toward zero in all the examples.
154
ARMA(l.l
1.0
1.0
pacf
acf
~kJ-
-1.0
k
-1.0
ARMA ( 1 , 1 )
1.0
1.0
acl
P
pacf
~k
k
k
-1.0
-1.0
ARMA ( 1 , 1 )
1.0
'.0
pacl
acf
P
k
k
~k
-1.0
-
k
1.('1
ARMA ( 1 , 1 )
1.0
1.0
pacl
acf
P
~k
k
k
k
.
-1.0
-1.0
ARMA ( I, 1 )
1.0
1.0
pacl
ad
P
k
-1.0
k
~k
k
-1.0
Examples of theoretical .acf's and pacf's for ARMA(1,1) processes
155
IV
Seasonal ARIMA nrocess,ARIMA (p,d,q) X (P,D,Q)s:
The seasonal ARIMA modelling follows
used for non seasonal data.
difference
observations
variations.
(Y t - Y
procedures
Wi th seasonal data we must often
by
length s according
to
the
seasonal
This involves calculating the periodic differences
).
t -
the same
If we have
monthly data then s = 12 or if· daily
•
data then s = 7 and so on.
For the theoretical acf and pacf of seasonal processes, we
do the same as for the non-seasonal data. At the identification stage
the
estimated acf and pacf are calculated from the available
data and compared with some common, known theoretical acf's and
pacf's and a tentative model is chosen based on this comparison,
then the parameters of this model are estimated, and we continue
the same procedure as in model building procedures of nonseasonal
data.
But the coefficients appearine at lags 1, 2, 3,
in non
seasonal acf and pacf, appear at lags 1 s, 2s, 36, ....
in purely
seasonal acf and
pacf.
For elCample in a stationary seasonal
process with one seasonal AR coefficient and seasonal period s. we
note that theoretical acf decays exponential but at the seasonal
lags
1s, 2s, 3s, .••
only.
In the following we present the main outlines of the seasonal
ARIMA processes:
Seasonal MA(Q)s model of order Q is
y
t
a
t
-
e I a t-. _ e 2 a t-2.
- ....... - 9
Q
a
t -
( 13 )
Q.
The acf will be nonzero only at the seasonal lags of Is, 2s,
...
,
Qs, and.
for k c I. 2 . .. I Q
222
1 . 9 . 9 ....... 9
I
2
Q
156
the seasonal
MA(Q)s model can be considered as a special case of the
non seasonal MA model of order q = Qs, with non zero
0 - coeffi-
cients only at the seasonal lags ls, 2s, ... , Qs.
Seasonal AR( p)s model:
<I>
V
t
I
v
t -
+<1>
5
2
v
t -
+
25
+
cl>
p
v
t -
ps
This model can :,,, considered as a special case
model of order p=Ps
,with nonzero
( \4 )
+a
t
of non-seasonal AR
</> - coefficients only at the
seasonal lags ls, 2s,· .... Ps
Stationarityand inverti;'ility
the
same
seasonal
as
conditions of the above models are
in the nonseasonal models.
models
·...e
apply
For
the
to
the
separately
multiplicative
seasonal
and
non seasonal components.
For the nonstationary seasonal ARlMA models, we take the seasonal
difference of period
s for
{Y t}
•
As a special case, the autocorrelation function of
the
seasonal AR(1)s model is given by
Pks
=..r.!<
'!"
for k = 1,2, ....
(15 )
with zero correlation at all other lags.
Por further details on the seasonal ARlMA process, one can
refer to any standard text book related to this subject.
157
5.3
ARMA MODELLING FOR SELECTED DATA:
5.3.1 MODELLING THE DAILY ACCIDENTS, INJURIES AND FATALITIES
IN RIYADH AREA:
In this section we consider the dany data for the above
three variables,
in each case seeking a time series model which
gives an adequate
includes
representation of
general ideas
of
time
the
data.
series analysis,
The
discussion
and
particular
consideration is given to ARMA and ARlMA ,models with seasonality
being taken into account where it seems appropriate.
I
DAILY ACCIDENTS IN RIYADH AREA "C2":
The data are given in Table (3-1), and a time series plot of
this data is shown in Fig. (5-1).
A visual examination of this
plot provides the initial ideas as to the type of model likely to
be appropriate.
In this case we note that there is a very slight
suggestion
an
of
increasing time.
upward
trend
(approximately
linear)
with
However, it was concluded that the trend, if one
was indeed present,
was so small that it could safely be ignored.
The acf and pacf of C2 are given in Fig.
(5-2) and Fig.
(5-3)
res pec t i ve ly.
Examination
mean-stationary,
of
the
together
series
with
the
C2,
now
assumed
corresponding acf
to
and
be
pacf
(note lag7, 'lagl4, lag21 , ••• ) suggests the existence of a day of
the week effect.
To remove this it is necessary to find the daily
,
d7 and
a
is by a one-way ANOVA procedure.
Xt
= Yt
convenient "flay to
lie now define
- ds
where Yt is the observation at time t
t = " 2,
, 708
and
s = t mod 7.
achieve
this
158
rep~t
ti7
~:1e
Sunday,
Monday,
.•• , Saturday <\>illy effects, and tests can <10" be ~'I,c;.·d
Ollt in
an obvious way to see ·.hether '\ai1y differences do indeed exi:,t,
day-of-the-·... eek
affect
removed
The se ries with
t.
r"'~
,,,,,I if so which days stand out from the
{Xt} and
corespilJ.~8
the
ds
values are given in Table (5-1) !lrd t11e results have an obvious
physical
Riyadh
GO
lo.terpretation in view of
area
(the
"weekend"
effect
rres ponding to Thursday and
clle ",' 'Les
the res'll t
{X t }
h~,\'riou
the kno .. "
of
high
~"3
Friday) •
(represented
in
accident
the
rRta~
time se ries plo t of
in MINITAB by C20)
is
given in Fig. (5-4), and the >lcf "11:1 p"cf for C20 are given in
Fig. (5-5) and Fig. (5-6) respectively.
the
last
r'emaiM,
two
and
diagrams
the
that
main achievement
17 has been to mak"
l(ould expect.
d"eo';""ts
~hH
p'lcf
of
A caref"l ;.'\~pection
some
daily
of
effect
taking Ollt dl,
... ,
d2,
lag 7 value much smaller,
A careful inspeGtion ,)f 'i'ie-
still
/lS
we
(5-5) and (5-6) can
give a hint to use an AR(6) model which ,has the form
x=~.
to]
t-l
•...•
~x
6
t-6
••
t
Since the :O\INITAB package is not al!1enable to AR models of
order higher than 5, this ...as fitted by a multiple regression procedure 'is detailed in Fig.
now represents
the
daily effect) and C2-C7 the corresponding lagged varia:'1",,3.
1:'1
respons"
(5-7) .... here Cl
v'1~iabe
addition to giving the fitted mo,\el, Fig (5-7) also show the acf
,)f the fitted residuals.
residua1s are randomly ,lili trlbuted.
It will be note<l that these
139
Model diagnostics
The R2 criterion is small "".1
t.hl03
;.",licates
correlations bebeen these observations are small ('l.~
The
t-ratio
for
the
(correspon,li"e ~,)
constant
,~'"
and
the
coefficient
that
; 13%).
of
C3
1<1g 2 term of C20) are not signifi-
cantly different from zero, so these tens can be excluded
from the model.
Fig.(5-8).
Details of the modified model are
The Portmanteau statisti.c Q* values are
si.'r~<l
L-t
not Given. in
the
0utput, but calculated separately the results are
~t"r'\ld
given in the follol<llrte; table.
Table (5-2)
leg
Q*
12
24
36
48
14.37
23·7'5
44.·)7
58·99
18
30
42
34.81
50.89
69.31
6
d. f.
2
16.81
X
0.01
From Table (5-2) we see that the Q* 'ralues are not
B ignificantly larse, 90 this tes t lends support to the sugge" tion
that this model gives a satisfact'H'Y ~eprsntaio
for the given
data. The acf, the histogram and the time series plot of the residuals
in Fig. (~-8)
indicate that the residuals are randomly distributed.
The effect of removing the constant (~ o ) '-'rt,\ C3 (x ._ 2) is
shown in Fig.(5-8).
As expected, the remaining coefficients
ch ... nge very little and in fact
the final v.. r"i.on of the fitted
model is closely approximated by
x
t
= 0.1
(X
.
t-l
+
x
t-3
+
x
t-4
+
x
t-S
) +
0.16
X
t-6
( ,5 )
An alternative, but e"""ntially equivalent, approach to this
problem is to fit a seasonal model of period 7.
"
160
The
best
ARIMA model
(0,1,1) X (0,1,1) 7 for C2,
to
fit
the
given
data
is
ARlMA
details of this model are gi'lan in
Fig. (5-9).
From the Fig. (5-9) we note the following:-
All
•
the Q
values
are
rlot
significantly
large,
so
this
test supports the suggestion that oUr model is sui table for
the given data.
All the cOl"relations of the acf of the l"esiduals are less
than 0.1,
so we can say that
the
t"esiduals are randomly
distributed and follow a normal distribution as-indicated by
the - histogram of
the
residuals.
Plot
of
rlorr.lal
scores
against the residuals is close to a straight line. Plot
of
the residuals against the predicted values support the suggestion that the residuals are normally distributed,where
no pattern can be observed, which indicates a good fit.
The final version of the model is
Y
=
(
•
t
-
0.92.
t-l
)
(.
t
-
0.98
•
t-l
( ,6 )
161
II
DAILY INJURIES IN RIYADH AREA "C3":-
The da ta of C3 are given in Table 0-1).
From the
time
series plot of C3, as given in Fig.(5-10), we note that there is a
slight upward trend as the time t increases.
In !l.ddition, there
is a small upward shift from t=360 to 416, and this could be due
to some natural effects in that period which corresponds to the
first and second month of 1983.
In.ny case this small shift will
not give a big effect on the behaviour of the time plot.
As before,
first differences are used to
remove the
trend
and the plot of the first difference C33 is given in Fig (5-11).
It is clear from this
figure
that the
time series is
now mean
stationary, so we can begin to examine this data.
The acf and pacf of C33 are given in Fig (5-12) and Fig
(5-13) respectively.
It is
follows
clear from
the acf and pacf of C33 that the data
a MA model, because in the acf in Fig. (5-12),
r1 has
a large value and the rest of the values are small.
Also from the
pacf
exponentially
in
Fig.(5-13)
decreasing as
the
the
lag
pacf
k
values
increases,
are
but
slowly
there
extreme values such as the lags 20, 25, 27,
negative
values
between
-0.092
and
-0.061,
are
still
some
and 28, which have
and
this
may
be
to
C33
or
resulting from the shift in the original data C3.
lie
will
equiva19~tly
Fig. (5-14).
begin
by
fitting
a
MA( 1)
model
IMA (1,1) to C3. the resulting output being given in
This output includes the following:"
162
acf of the residuals, which is denoted by C5, we note that
I
'k
I
<
for k = 1, 2, 3, . . . . This indicates that there
0.1
is no pattern of correlation between the different values of
rk'
and
So the
follow
residuals appear
the
normal
to
be
distribution
histogram of the res1duals.
randomly dis tri bu ted
as
indicated
by
the
A plot of the normal sco res
agains t the res1duals is close to a s traigh t line, and this
supports
the
suggestion
that
the
residuals
are
normally
distributed.
The t-ratio for the constant is not significantly different
from zero,
so
we
The
exclude it from the mode l.
revised
analysis is shown in Fig. (5-15).
All the values of Q*,
in Fig.
(5-15) are not significant
at the 5% level, and this supports our fitted model.
=-
The estimated MA parameter ';:1
value of r1
= -
0.530,
so there
0.4996,
but the actual
is not a big difference
\ie conaider the lMA (1,1) for C3 is the best model to fit
the data.
The fitted mode I
Y
t
= a
t
-
0.96
as
a
given in Fig (5-15),
is
( 17 )
t- 1
where
{at}
is
a whits
noise series,
which
is
a
sequence
of
independent, identically distributed random variables
note: in model 17 the estimated mean
it is very small
(#
= 0.0008 ).
,...
/l
is excluded, because
163
III
DAILY FATALITIES IN RIYADH AREA "C4":-
The data of C4 are given in Table (3-1).
As be fore,
the
time series plot is the first step in dealing with this sort of
analysis.
The time series plot of C4 is given in Fig. (5-16).
The first note on this plot is that there are no trends at all,
but many peaks exist.
These. peaks will
naturally
exist
in
this
sort
of
data
because some times. it will happen that one accident involving a
bus results in a large number of fatili ties at once.
But about
!lalf of the data have a zero value (346 observations out of 708
observations).
For this data there is no need to use differencing because
the data are mean stationary.
The acf and pacf of C4 are given in Fig.
It is noted that all ~
(5-18) respectively.
are
very
small
and
correlation is at I
the
'45
absolute
I = 0.081.
value
(5-17) and Fig.
for k=l,
for
the
In addition,
" ' , 50
largest
these ~
autovalues
do not follow any AR model or MA model or ARMA model, but seem to
be a sequence of independent random values.
So we sugges t
that
this data represents a white noise series.
Our time series is of length n=708, by using the result that
the standard deviation (s.d.) of
,0-
I
so the s.d. of
~
~
for a white noise series is
= 1/,;708= 0.038.
that about 95% of the estimates lie within
~
~)
..In
our
data
three
Therefore we expect
+
0.075 (~2
autocorrelation
functions
s.d. of
exceed
0.075, which are r 20 = 0.077, r33 = 0.076, and rH = - 0.081.
For the pacf of C4, we know that the white noise series can
be considered as AR(p) wi th P =0.
Quenouille' s result applies, and
~
164
2/
.rn
= ~
estimates.
0.075 can be used to judge the significance of the
From the pacf upto lag 50, of the data only two values
of<P k exceed ~
0.075, which are0;6
33
0.076 and
=
p45
= -
0.097.
So we decide that the number of fatalities en the Riyadh area
follow a white noise series.
We cannot go further than this in modelling the fatalities
of the daily data of Riyadh area
series are not capable of prediction!
,
as
the peaks
in
the
time
165
5.3.2 MODELLING THE MONTHLY ACCIDENTS, INJURIES AND FATALITIES IN
SAUDI ARABIA
As before, we try to fi t an ARMA or ARIMA model for the
given three variables.
The data are given in Table (3-6) for the
period of 144 months (12 years in the period of 1974-1985).
In
the following we will discuss each variable.
I
MONTHLY ACCIDENTS IN SAUDI ARABIA "C2":The first step in our analysis is examining the time series
plot of the data to know whether the time series is a stationary
process
or
The
not.
time
series
plot
of
C2
is
given
in
Fig.(5-19), and Fig. (3-1).
It is clear that
the plotted points are increasing in an
approximately linear manner as the time t increases, so this time
series is a non stationary one.
To get a stationary time series,
simply take the first difference of C2.
The time series plot of
the first difference "C21" is given in Fig. (5-20).
Now we have a
stationary time series.
The
acf
and
pacf
Fig. (5-22) respectively.
'are small except for r:z. I
of C21 are given in Fig.(5-21) and
For the acf of C21 all l'k for k
~
1
,while in the acf of C2 are large
values as given in Fig.(5-23).
And this attributed to differenced
process, where we have C21 a stationary process.
The pacf of C21
suggests that an AR(2) model is suitable for C21, (or equivalently
ARI (2,1) for C2), because more than 95% of the
in the dOmain of + 2/
vn-=
cP.
I(
for k
> 2 fall
+ 0.167.
The results of the fitted ARI(2,1) model to C2 ., are given in
Fig. (5-24). From the fitted model we note the following:-
166
All the values of Q* at
lags 12,' 24,
significant,
no
so
we
have
reason
36 and 48 are
to
reject
the
not
given
model.
rl
=
-
while ~1
0.175,
= -0.172
with s. d.
0.0836,
=
so
the estimated value of rl with its s.d. falls in the range
of rl with t-ratio
= -
,..
2.51.
r2 = - 0.18 , while r2 =
-0.1822
with s.d.
= 0.0836,
so
the estimated value of r2 with it's s.d. fall in the range
of r2 with t-ratio
=-
2.61.
The acf of the residuals
small
and
this
correlated.
"C5";
indicates
The
all
that
histogram
of
the
the
the
values
of IK are
residuals
residuals
are
appears
not
to
follow a normal distribution.
To make sure that the residuals are normally distributed, we
take the plot of normal scores against the residuals.
the residuals are normally distributed,
If
the plotted points
will be nearly on a straight line.
Our plot suggests this
is so,
residuals
hence we
can say that
the
are
normally
distributed.
A plot of the residuals against the predicted values does
not follow any specific shape and the plotted points fall in
a rectangular scatter diagram.
A time
series
plot
of
the
residuals
indicates
that
the
residuals are randomly distributed along the time axis.
The fitted model for "C2" is ARI (2,1)
can be written in
the following form:-
Y
t
=
-
0.2095
Y
t-l
0.2183
Y
t-
2
+ a
t
( 18 )
167
II
MONTHLY INJURIES IN SAUDI ARABIA nC3 n:
The time series plot of C3 is given in Fig. (5-19) and Fig.
0-1).
From this
stationary,
increases.
figure we note
because
the
that
observations
In addi tion,
the
time series is
increase
as
the
not
time
the acf of C3 (which is given in Fig.
(5-25) exhibits positive correlations with high correlations at
low lags.
The seasonal effect is very clear in the acf
which is evident at lags 12, 24, 36 and 48.
also appears in the pacf of C3, Fig.
of C3
The seasonal effect
(5-26).
So this data is
suitable to use seasonal ARIMA models.
The first
difference
of C3
(non-seasonal difference) was
taken and its plot is given in Fig. (5-27).
Now the time series
for C31 (the first difference of C3) is stationary and from this
plot we note that the seasonality is quite apparent, where the 1 's
tend to be low and B' s tend to be high.
All time
points are
carried out with a period of 12 specified, so that observations of
one period can be recognized.
The seasonali ty is displayed in the acf of the differenced
series as given in Fig.
lags
12,
24,
36
and
(5-28).
48 are
Fig.
decaying quite slowly.
Note that the correlations at
positive
correlations,
(5-29) and Fig.
which
are
(5-30) show what
happens if we calculate a period of 12 seasonal difference instead
of the nonseasonal difference.
The time plot in Fig. (5-29) shows
that most of the seasonali ty has been removed, and the series is
stationary with big variations at some observations.
Fig. (5-30) strongly indicates the seasonality.
seasonal and nonseasonal differencing.
difference is given in Fig.
use an AR model
seasonal effect.
for
the
(5-31).
The acf in
We will take both
The acf and pacf of this
This pacf suggests that we
time series and
a MA model
for
the
168
So our investigation will involve the seasonal ARlMA models.
We find that the best ARlMA model which can fit the given time
series is ARlMA (2,1,O)X(O,1,1)12.
The computer output is given in Fig'(5-32).
From this output we note the following:All the Q* values at lags 12, 24, 36 and 48 are not significant, so we have no reason to reject the given model.
The acf of the residuals "C5"; all the values of IK are
small except for rand r
7
effect.
scores
because of the seasonal
28
Histogram of the residuals and plot of the normal
of
the
residuals
against - the
residuals
itself
indicates that the residuals are normally distributed.
A plot of the residuals against the predicted values does
not follow any specific shape and the plotted points fall in
a rectangular scatter diagram.
The final version of the model will be
y
,
(
-
0.53
y
'-I
-
0.17
Y
t- 2
+ a
t
(a
t
-
0.85
a
t- 1
( 19 )
169
III
MONTHLY FATALITIES IN SAUDI ARABIA "C4":-
A time series plot of the fatalities is given in Fig. (5-19)
and Fig. (3-1).
From the initial examination of this plot we note
tha t the plotted points are increasing as the time increases, so
this time series exhibits an approximately linear trend.
and
pacf
of
respectively.
C4
are
given
in
Fig.
(5-33)
and
The acf
Fig.
(5-34)
The seasonal factor is very clear at lags 12, 24,
36 and 48, so we need to use the seasonal ARIMA models to fit a
suitable model.
The differencing process is needed to make the time series
stationary.
We take the difference with d=1 and the time series
plot of the differenced series is given in Fig. (5-35).
All
the
following
analysis
differenced series. From Fig~5-J)
will
be
in
Ef
we note that
and l ' 03 tend to be .low,
.This indicates
terms
of
the
tend to be high
the seasonali ty which
also appears from the acf and pacf of the differenced series as
given in Fig. (5-36) and Fig. (5-37) respectively.
the
seasonal
effect
difference of C4.
given
in
Fig.
seasonality
is
into
account
and
make
We will take
the
12th
order
The acf and pacf of this differencetl se des are
(5-38).
evident,
From
so
we
this
figure
need
to
take
we
note
the
that
the
seasonal
and
non-seasonal difference in model fitting.
We fitted two multiplicative seasonal ARIMA models, namely
the
ARlMA (2,1,0) X (0,1,1) 12 for C4 as given in Fig. (5-39) and
also
ARIMA (3,1,0) X (0,1,1) 12 for C4 as given in Fig. (5-40).
We will make a comparision between these two models.
170
All the Q* values for the given d. f.
for both models are
not significant.
The acf of the residuals shows that all the correlations for
the second model do not exceed±2/vn = ~
While for
0.lb7 •
the first model there are two correlations at lags 3 and 6
which exceed
~
0.167.
So we decide that the second model is
more appropriate to fit the given data.
A histogram of the residuals,and a plot of normal scores
against
the
residuals
support
the
suggestion
that
residuals are normally distributed for the second model.
the
So
our model will be in the following form:
Y
t
=(-O.6IY
t-l
-0.4l7Y
t-2
-O.28IY
t-3
+.)(.-0.874.
t
t
t-l
( 20 )
171
5.3.3 MODELLING THE MONTHLY ACCIDENTS, INJURIES AND FATALITIES IN
RIYADH REGION
The number of accidents, injuries and fatalities are given
for the Riyadh region over a period of 12 years, month by month,
in Table (3-7).
So we have 144 observations for each variable.
Time series analysis is sui table for this number of observations.
We will carry out the same procedures as before for the daily data
of
the
Riyadh
area.
MONTHLY ACCIDENTS IN RIYADH REGION nC2 n :_
I:
The time series plot of C2 is given in Fig. (5-41) and Fig.
(3-2) and i t exhibits a special behaviour with time t.
In the
first 17 months the number of monthly accidents on average, was
less than 600.
In the periocl of 18-122 months,
the numbers of
accidents were between 600 and 900 accidents, with 7 months less
than 600 and another 4 months more than 900.
123-128 the
number
increased
to more
From month number
than 900,
after that
it
decreased from the month number 129-134 to be less than 900, then
it
increased again
to
more
than 900 accidents
in
the
last 8
months.
In general, if we take the number of accidents with time,
this will be
~liBhty
increasing.
First however, let us examine
the acf and pacf for the row accident data.
The acf and pacf of nC2 n are given in Fig. (5-42) and Fig.
(5-43)
respectively.
From
the
acf
we
note
high
positive
correlations at low lags which suggests an exponential decay as is
clear from the figure.
The pacf suggests an AR(l) model because
for the pacf '" kk for AR(p) ., theoretically,
"'kk =
q for
k
>
p.
172
We have n = 144 and ~
Vn
2/
=
~
0.167,
thus none of the
pacf values are significantly different from zero for lags beyond
With such a strong lag 1 correlation and the increasing time
series plot at different points, I(e can consider a nonstationary
model with d = 1, the acf and pacf of the first difference of C2,
C22, is given in Fig. (5-44).
There is no clear evidence that any
type of model can fit this differenced series, so the AR(1) appears
to be our first choice to the original data C2.
The results of fitted AR(1) model to C2 are given in Fig. (5-45),
including some tes ts oa the residuals.
From Fig. (5-45) we note
the following:-
For Q* values (The modified Box-Pierce statistic), we find
that
all Q* values for 11,23,35, and 47 degrees of freedom (d. f.) are
not significantly large, so we can not reject the hypothesis that
the given model is appropriate.
- The values of the acf of the residuals "C5" , in general, are small
and do not exceed + 2 /
against
~
=
0.167 except the correlations at
Histogram of the residuals and plot of normal
lags 1 5 and 35.
scores
rn
the
residuals
normally distributed.
indicate
that
the
residuals
are
This supports the idea that our model is
the desired one.
-The t-ratio of the constant is high, so we cannot excluded it from
the model.
The final version of the fitted model I(ill be
(Yt - 729.32)
(Y
= 0.5809
.-1
729.32) + 108.713+ at
or
yOt
= 1261.7
+ 0.58 Y
+
.-1
at
where
{ at} is a whi te noise series.
( 21 )
173
II
MONTHLY INJURIES IN RIYADH REGION "C3":-
The
time
series
plot
Fig.(5-41) and Fig. (3-2).
of
the
injuries
C3
are
siven
in
The behaviour of the time points looks
like the behaviour over time of the accidents discussed in the
last section, where we have in the first 17 months an increase in
the number of injuries, but less than 270 injuries ia the month,
the mean value of this 17 months is 165 and the mean value of all
the data is 301
which
is
much la rger
than 165.
This
figure
reflects how much is the difference between this part and all the
data.
So we can consider this
time series plot as a stationary
time series from t=18 to t = 144.
The acf and pacf for the complete data set are given in Fig.
(5-46) and Fig. (5-47) respectively.
We note from the acf that it
is decayiag exponentially as lag k increases with high positive
correlations at low lags.
addi tion all
+
2 /
vn
= ~
the
pacf
0.167.
The pacf suggests an AR (1) model.
beyond
lag k=l
fall
in
the
domain
In
of
But when we fit AR(l) to C3, we find that
all the values of Q* for 23, 35 and 47 d. f.
are
significantly
large, so we must look for another model.
In addition, the acf of
residuals at some correlations are high.
The same happened for
higher orders of AR(p), that it is significantly large.
If we consider the differencing process vi th d=l,
the time
series plot of this differenced series is given in Fig. (5-48).
Now we have a stationary time series with acf and pacf given in
Fig. (5-49).
positive
Most of the correlations are given in negative and
order.
In
Fig.
(5-49) ,
original acf of C3 is highly positive.
as
rl
= 0.-321 ,
while
0.167 all
+ 0.167 except for
"'3
"'kk
for k
~1
the
We can fit AR (1 ,1) to C3
indicated from the pacf of the differenced series,
+ 2 / vn= ~
in
and
for
fall in the domain of
But in the model fitting process of
174
ARI (1,1) for Q* = 68.2 at 35 d.f ,md /
is
0.001
(35)
=
66.55.
SO Q*
significantly large and we must look for another model.
For
higher orders of AR(p) models, we find that Q* is significantly
large.
So AR(p) for
series.
p ~
1 can not be use for our differenced
Mixed models are tried, and we found that ARH!A (3,1,1)
for C3, as given in Fig. (5-50), can fit our data.
of Q*
are
not
significantly
All the values
large and we are
not
lead
reject ·the hypothesis that this model can fit the given data.
acf of the residuals, in general, are
Histogram
of
distributed.
the
We
residuals
small except r
20
exhibit
can check the
that
no rma l i ty of
to
The
= - 0.171-
it
is
normally
the
residuals
by
plotting the normal scores of the residuals against the residuals
itself .
So if the residuals are normally distributed then the
plotted points should fall approximately on a straight line.
This
plot is included in Fig. (5-50) and the points in the plot fall on
a line except few points,
and
this could be attributed to SOme
extreme observations in the differenced series.
The fitted model for C3 will be
Y = 0.26 Y
t
t-l
+ 0.07 Y
t-2
- 0.26 Y
t-3
+ a
t
-
0.7
•'-I
( 22 )
If we remove the first 17 observations from the analysis we
find a stationary time series and it' s acf and pacf are given in
Fig. (5-51) and Fig. (5-52) respectively.
We find that AR(1) model is suitable for this series,
computer
Olltput
of
AR(1)
for
observations are given in Fig.
(Y - 318.57 ) = 0.521 (Y
t"
Y
t
0.521 Y
t-l
+
t-l
305.2 + •
C3 after
removing
first
17
(5-53) and it is model will be
- 318.57) + 152.608 + a
t
the
the
t
( 23 )
175
III
MONTHLY FATALITIES IN RIYADH REGION "C4":-
A time series plot of the fataliti.es C4 is given in Fig.
(5-41) and Fig. (3-2).
This time series is not stationary in the
mean, because there is an increase over the first 17 observations,
and there are big variations in the
plot as is very clear from
the observation number 38 to 48 and other smaller variations in
different parts of
the
plot.
So we cannot
make any kind
of
analysiB before we take differences to change the time series to a
stationary one.
The
acf and pacf of C4 are given in Fig. (5-54)
and Fig. (5-55) respectively.
The time series plot of the differenced series C41 is given
in Fig. (5-56).
Now we have a stationary time series.
and pacf of the differenced series are given in Fig.
Fig. (5-58).
The acf
(5-57) and
A careful inspection of the acf and pacf of C41 can
suggest which kind of model we can use to fit our data.
From the
acf in, Fig. (5-57), we note that the correlations die out quickly
after lag 2 and in the
values are dying slowly.
pacf in Fig.
(5-58).
In general,
the
So we sugges t the use of a MA mode 1 of
order 2 to fit the differenced series.
In other words, "Be lMA
(1,2) for C4.
The computer output of fitting UlA (1,2) for C4 is given in
Fig. (5-59).
From this output we note the following:
All the values of Q* are not significant at
10; 22, 34
and 46
suggested model.
d.f.
So
this
lends
0:
= 0.05
support
to
and
the.
176
95% of the correlations of the acf of the re·siduals fall
wi thin .: 2
Ivn;
+
0.167.
To tes t the normaH ty of the
residuals, we take a plot of the normal scores against the
residuals.
The plotted points,
approximately,
fall
on a
straight line as we note in the given plot of normal scores
against the residuals.
95% of
within
\!lkk
for the pacf in Fig. (5-58) after lag 2 fall
0.167.
+
The fitted model for C4 will be
y
t
a
t
-
0.5779
a
t-)
-
0.2311
a
t-2
( 24 )
177
5.4
RESULTS AND DISCUSSION:
To discover the relations among the three variables under
the study for the three selected data sets, we must summarize the
fitted models which are given in section 5.3 .The fitted models
are given in tables (5-3), (5-4), and (5-5) as follows:-
Table (5-3)
Daily data of Riyadh area:Model type
Variable
Accidents
ARIMA (0,1,1)
(0,1,1) 7
Injuries
IMA (1 ,1)
Fatalities
White noise
Fitted model
Y
= (a
'
,-
0.92 a
, = a, Y, = a ,
Y
'-I
0.96 a
) (a -
0.98 a
t
t-l
)
'-I
Table (5-4)
Monthly data of Riyadh·region:Variable
Accidents
AR(1)
ARIMA (3,1,1)
Injuries
(after removing
the first 17
observations) AR(l)
Fatalities
Fitted model
Model type
IMA (1 ,2)
, = 1261.7 + 0.58 Y'-I + a ,
Y, = 0.26 Y
+ 0.07 Y
- 0.26
,-2
'-I
Y
a
+ at - 0.7
,=
Y, =
Y
305.2 + 0.521 Y
a
t
-
0.58 a
t-l
'-I
-
Y
,-3
'-I
+ a
,
0.23 a
,-2
Table (5-5)
Monthly data of Saudi Arabia:Variable
Accidents
Injuries
.
Fatalities
Model type
Fitted model
ARI (2,1)
Y
ARIMA(2,l,O)
(0,1,1) 12
Y
ARIMA (3,1,0)
(0,1,1) 12
, =-0.21
t
(a
t
Y
= ( - 0.53 Y
- 0.85 a
-
'-I
t-l
t-l
0.22 Y
,-2
'- 0.17 Y
t-
+ a
,
2 +a )
t
)
Y t = ( - 0.61 Y t- I - 0.42 Y t - 2 - 0.28 Y t- 3
(a,-0.81a,I)·'
'I
178
For the ARMA modelling of the given data, no one type of model
can be found to describe the behaviour in each case for anyone of
the three variables included in the study.
The
seasonal
factor
has
a
marked
effect
on
the
model
behaviour for the following variables:accidents of the daily data of Riyadh area, where we have a
day of the week effect, i.e. the seasonal period s
=
7 •
injuries of the monthly data of Saudi Arabia, where
the monthly effect, i.e. the seasonal period s
have
~e
= 12.
fatalities of the monthly data of Saudi Arabia, where we
have the monthly effect, i.e. the seasonal period s
For the above three
process
which
is
difference period D
moving
~
we have the same seasonal
models
average
= 12.
with
parameter
Q
and
1, with different estimated parameters
The accidents in Saudi Arabia and Riyadh region follow the
AR process, with different values of
where for Saudi Arabia our
~
model follows ARI (2,1) and for Riyadh the model is AR(1).
The accidents, injuries and fatalities of the monthly data
of Saudi Arabia
follow a fixed
process which
is
the
AR
process but with parameter p = 2 for the accidents and injuries
models and parameter p = 3 for the fatali ties model.
models are given with difference d
=
1.
All these
179
ARMA
model
of
the
injuries
in
Riyadh
region
is
an
interesting case, where we find that the ARIMA (3,1,1) model can
fit the given data, but if we remove the first 17 observations
from
the
series
our
model
will
be
AR(l),
and
this
can
be
attributed to the following:
The series is a stationary time series from the observation
No.18 on wards while i t is not stationary i f '.. e take i t as one unit
wi thout any di fferencing,
as is clear from Fig. t3-2) and Fig.
(5-41) •
Another case is the number of fatali ties of the daily da ta
of Riyadh area, where it follows 'a white noise model, but if we
take the first difference (given that the series is stationary),
the acf and pacf of the
differenced series are
given in Fig.
(5-60), which suggest that MA(l) process can fit the differenced
time
series,
fatalities.
(5-61 )
or
IMA
(1,1)
process
for
C4,
the
number
of
The ARIMA procedures for this model are given in Fig.
which
shows
tha t
the
res iduals
are
not
randomly
distributed, or do not follow the normal distribution as
is
clear from histogram of the residuals and plot of normal scores of
the
residuals
against
the
residuals
itself,
so
we
hypothesis that out time series follows an IMA( 1,1).
try any AR process,
even the acf of the
reject
the
We cannot
because the acf of the differenced series,
original series do
not
recommend that
we
should fit an AR model to the given time series.
Se we say that the white noise model can fit the number of
daily fatalities in the Riyadh area.
180
Accidents
and
injuries
of Riyadh area and
fatalities
of
Riyadh region follow the MA process, with different orders, where
it is of order q = 1 for accidents and injuries of Riyadh area and
of order q
2 for the fatalities of Riyadh region.
=
The following table summarizes the ARMA process for the three
sets of data under study of time series analysis.
Table (5-6)
Injuries
Accidents
ARIMA (0,1,1)
(0,1,1)7
Riyadh area
This
model
White noise, AR( 0)
ARIMA (3,1,1)
or AR(l)*
,..MA ( 1 ,2)
ARI (2,1)
Saudi Arabia
*
IMA (1 ,1)
AR( 1)
Riyadh region
Fatalities
is
ARIMA (2,1,0)
(0,1,1) 12
ARlMA (3,1,0)
(0,1,1) 12
true
after
removing
the
first
17
observations from the series.
As
noted in
the previous discussion, it is difficult to
arrive at a fixed process that can help in fitting the number of
accidents,
words,
injuries and
fatalities
in Saudi
Arabia.
In
other
there is no fixed process that can be generalized to any
variable of the above three variables as a basic step in forecasting
the
posi tion
of
road
fatalities in Saudi Arabia.
traffic
accidents,
injuries
and
181
Daily accidents of Riyadh area after removing
day of the week effect
-------,
THU
SUN
SAT
MON
FRl
TUE WED
Table (5-1)
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2. 376
-2.624
B. 376
-7.624
-18. 624
-4. 62011
-9,62-4
3.376
19.376
-3. 624
1.376
7.376
9.376
6.376
-11. 62-4
15.376
18.376
-7.376
3.376
15.376
B.376
9.376
11.376
14.376
-2.624
-7.624
9.376
-5.624
7.376
-1. 62011
3.376
10.376
10.376
-9.624
18.376
26.376
13.376
1. 376
12.376
7.376
12.376
7.376
1.376
12. 376
9.376
-4.624.
8.376
-5.624
3.376
-2.624
-113.624
2.376
12.376
1.376
-0. 62011
6.376
7.376
-4. 6~q
-0.624
-3.6~4
-6.624
-8.62011
1.376
32.6
i
I
I
I
Ii
"
4e.9+
lIIe. I .
21.
a•
• ______ + ______ • ______ + ______ + ______ + ______ t- ______ +______ +______ •
•
1
,'4
21
28
:I,
42
.. 9
:Sol.
63
______ • ______ • ______ • ______ • ______ • ______ • __
7e
77
I..
91
98
115
----.------+------.------+------.------+------.------.------+------.------+------+
112
119
126
III
1'18
147
154
161
168
175
18:!
189
, •. a..
"8. a.
21.
e•
•------+------+------+------+------+------+------+------+------+------+------.------+------+------+------+------+------+------+------..
------+------+------+------+------+------+------+------+
I"~
21U
218
211
224
231
238
245
2:S:.!
2'9
266
273
288
2B7
294
381
lea
31'S
J2~
J:::9
336
343
J:i8
J~1
36"
311
378
la'
00
N
"',1+
48.
a.
21. I .
+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------+------.------+
31:1
J92
399
406
4ll
421
427
414
441
448
4:1:1
462
469
476
401
4911
497
:584
:Ill
:U8
:52:1
:532
:119
:546
:1:11
:S611
:567
371
4 •• ' ·
21. I .
+------+------+------.------.------+------.----_..:.------.------+------+------+------.------.------+------+------.------+------+------.------+------+
:574
:581
:S18
59:1
6it:;:
619
616
623
631'
637
6"14
6:11
6:18
66:5
672
679
686
69:<
188
181
114
:567
Fig(5-1)
Time series plot of the daily accidents in Riyadh area.
183
ACF of C2
--1.0 ·-0.8 --0.6 ·-0.4 --0.2
.. -
:I.
2
3
4
5
6
7
8
S'
10
11
1"
13
14
15
16
17
18
~
1<;'
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
-
- •• j.+ •• -
- •••• ~
........ -
-
0.0
0.2
- - .. - - - , . . . . . , . - - .. -
XXX XXX
XXXX
XXXXX
XXXXX
XXXXX
XXXXXXX
XXXXXX
XXXXX
XXX
XXXXX
XXXXX
XXXXX
XXXX
XXXXXX
XXX
XXX
XXXX
XXX
XX
XXXX
XXXXX
XXX
'XXX
XXXX
XX
XXX
XXXX
XXXXXX
XXX
XXX
XXX
X
XX
XXXX
XXXXX
XXXX
XX
XXX
XX
X
XXX
XXXXXX
XX
X
XX
XX
XXX
XXX X
XXX X
XX
0.204
0. 105
0. 167
a.177
0. 148
0.233
0.209
0. 14,~
0.070
0. 174
0. 142
0. 153
0.110
0. 138
0.084
0.099
0. 133
0.086
0. 047
0. 133
0. 168
0.0?0
0.065
0. 131
0.053
0.071
0. 117
0.207
0.095
0.034
0.076
0.015
O,022
0.102
13. 152
0. 135
0.047
0.037
0.023
0.009
- 0.082
0. 139
12).022
0.015
0.050
0.051 .
0.069
0. 107
0.131
0.0'19
Fig(5-2)
0.4
0.6
- - - ~ ••• - - - -., •• -
0.8
•• -
1.0
_.J-- _ ...... ,.
..
ACF of the daily accidents in Riyadh area.
184
PACF of C2
-1.0 ·0.8 -0.6 ··0.4 -0.2
1
2
3
4
5
6
7
8
9
1O
11
12
13
14
15
16
17
18
19
2O
21
'")',
"-"-
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
0. 204
0.067
l~.
139
0.122
0.082
0. 173
0.113
0.050
···0. O38
0.03,S
0. (»24
0.054
·0. 009
0.077
·0. 026
0.012
0.028
··0.035
·0.034
0.043
0.087
··0. 005
··0. 003
0.041
··0. 031
-0.002
0.023
0. 125
0.014
0.017
·0. 026
·0.032
~·0.
~-.+,}
052
··0.005
0.076
0.031
··0. 004
0.017
··0. 044
·0.076
··0. 012
0.112
·0. 039
·0. 016
··0.008
0. 015
0.032
0.007
0.067
··0.014
Fig(5-J)
0.0
0.2
XXXXXX
XXX
XXXX
XXXX
XXX
XXXXX
XXXX
XX
XX
XXX
XX
XX
X
XXX
XX
X
XX
XX
XX
XX
XXX
X
X
XX
XX
X
XX
XXX X
0.4
0.6
0.8
1.0
-}
X
X
XX
XXX
XX
X
XXX
XXX
X
X
XX
XXX
X
XXXX
XX
X
X
X
XX
X
XXX
X
PACF of the daily accidents "C2" in Riyadh area.
8.8-·
• 20. 0"
"-'"
-i-......._......•. _... ___ --_i_········ _i· _____ ----i· -. _. _-. -..... -..... -
_ •. _•.•. _ .. -••.••.•••.• _ ... _. __ •• _ ...... _._ - _. _ ••• +_. - _____ •• _________ ......... _.•
I
18
28
31
48
68
~8
18
ae
'ilO
189
119
128
i · - - _ • . • • • _ . . . . _ • • ___ • i _. __
138
l-CIa
A
____
1:;8
..
__ A
168
______
•
_________ •
178
la0
211.8.
B.8+
+_ •• ___ ••• _ ... _. _ ••• - .... -. - -. -- -- •• ------- - .. -- ------- .. ---------..... - -- ............ - - - -- - •• -- •. -- - •••
tal
198
288
2111
228
230
248
258
268
i · - • -- - ___
278'
+ __ •• _. ___ +. __
2ee
298
------1 .... _._._ .. _..... __ .... t_-·-..••• __ ..... __ .•••. _
38~
318
338
3Z8
i __ . ______ • _________ •
34e
3:i8
368
CZI
28.8t
8.0'
-28.0'
36:' - . . . . - ;~
.•.. --. ;~
.. -. _ .. ;~
- -- _. -- ;;;----. -;~
--- -- .-;~
- .. - -. -. ;~-
--. - .. -;~
--._ .• ;;;. - .•. -~;
-' •• ---;;;-------;;;..... - -.-. ;~
- .. - -. -;~
... _. -;~
- - __
A
-
-
;;;.
-~;
---
28.' i
8 •••
-
• 28. 1-.
.. _.
._ .•• ___ .... _.••.•.•.•• _ •.• _•. + ...•.•• _ •••• -1,-,_, _._._._ ..... _: ••• ___ •
~
Fig. (5-4)
~
~
-
...
_+_- __ - - •• - ..... -.- ••••
-'T' _ .••••. _.•. ~;
. . - _ ••• ~;
•••.•. - - - •• ~;
-
- . ' - -- - - - i - - .
•••
. .
,.
._. __ ._ • • • • • _ •••••• - - , . _ •• _ • • " i - _ . • • •
".
•••
·_·t··
"
n.
Time series plot of the daily accident9 in Riyadh 6Xea after removing the daily effict.
-;~
186
ACF of C20
-1.0 -0.8 -'0.6 -,0.4 -,0.2
I-
J.
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
13
1<;'
20
21
22
23
24
2!5
26
27
23
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
43
4<;'
50
0.214
0. 150
0. 1<;'5
0.207
0. 1<;'5
).244
0.143
0. is,S
0.110
0.200
0. 170
0.201
0. 10<;'
0. 120
~1.
087
0. 141
0. 157
0. 109
0.086
0.134
0.0<;'<;'
0.095
0. 104
0. 154
0.073
0.11:3
0.118
0. 140
0. 101
0. 125
0.0<;'5
0.031
0.058
0. 103
0.080
0. 144
0.087
0.107
0.040
0.044
0.078
0.119
0.022
0.055
0.066
0.068
0.108
0. 106 .
0.057
0.052
_M -
M.....
~
- - - ..... - '. -
I·
_'N
'.
'.
t. -
0.0
N'_'
0.2
··.t. - •.•. N.t-
0.4
0.6
0.8
1.0
••.•• N ••• : •••••.•••• ,... ___ •• ,.. ___ ....
XXXXXX
XXXXX
XXXXXX
XXXXXX
XXXXXX
XXXXXXX
XXXXX
XXXXX
XXXX
XXXXXX
XXXXX
XXXXXX
XXXX
XXXX
XXX
XXXXX
XXXXX
XXX X
XXX
XXx X
XXX
XXX
XXXX
XXXXX
·XXX
XXXX
XXXX
XXX X
XXXX
XXX X
XXX
XX
XX
XXXX
XXX
XXX XX
XXX
XXX X
XX
XX
XXX
XXXX
XX
XX
XXX
XXX
XXXX
XXXX
XX
XX
Fig(5-5) : ACF of the differenced series of the daily accidents "C20".
in Riyadh area after removing the daily effect.
187
PACF of C20
-1.0 --0.8 -0.6 --0.4 -0.2
.. - -
l.
2
3
4
5
6
7
3
9
10
11
12
1:5
14
15
16
17
13
1S'
20
21
22
23
24
...,eL..J
26
27
28
-)('
L'
30
31
32
33
34
35
36
37
38
3S'
40
41
42
43
44
45
46
47
48
4S'
50
- -)0 •• - - - .. -
0.214
0. Hl9
(a. 152
0. 139
0. 111
0. 158
0.018
0.051
- 0. 01S'
0. 101
0.048
0.094
.. 0.017
0.006
-0.035
0.023
0.054
-0. 010
0.006
0.038
0.006
---0.017
0.00S'
0.071
-0.017
0.036
0.025
0.050
- 0. 001
0.028
0.002
-0. 033
-(a.021
0.005
0.014
0.075
0.012
0.042
- --_ . . " , -
••• _.,. _ ••
0.0
·····1· --.-
0.2
w'}"
0.4
-,- ..•• ~ ... -,
0.6
0.8
1.0
",-1' _ ... ,. -} - - -· ... 1.
XXXXXX
XXXX
xxxxx
xxxx
xxxx
xxxxx
x
xx
x
xxx x
xx
xxx
x
x
xx
xx
xx
x
x
xx
X
:x
X
XXX
X
xx
xx
xx
x
xx
x
xxx
xx
x
.. 0. 055.
-0.056
- 0. 007
0.058
--0.041
0.005
x
xxx
x
xx
xx
xx
x
-xx
xx
x
0.022
-0.001
0.046 0.013
0.020
-0. 022
Fig(5-6)
xx
x
xx
x
xx
xx
PACF of the differenced series of the daily accidents "C20"
in Riyadh area after removing the daily effect.
188
Fig(S-7)
Multiple regression procedure of the fitted model of the
da.ily a.ocidents "C2" after removing the daily effect.
>
lag cl
c2-c7
> regr cl 6 c2-c7;
SUBC> residual cB,
M-I'D
M18
The regression equation is
Cl = 0,~49
~0,115 C2 .-~,032B
C3 {- O,0999 C4
+ 0.160 C7
102 cases used 6 cases contain Missing values
Coef
0'\;)9
0, 11534
O,O3231
0, 099B6
0, 11'106
0, ~'10:0, 1:5'1'19
F'red iCt.OI'
Const.ant
.-
CJ
Cll
CS
e(;'
C7
s = B,420
C5 { O,0910 C6
~,14
t- ratio
St.dev
0,Jl/3
I c:'
lil. ._,.)
3, ~8
O,O3748
0, 0372i'
0, 0J7~36
0, 0:1/ 6f.;
0,()(3
~J,
C")
~-
0,~3742
~,
6B
"
:~
,
g~5
2.42
4. 2\~)
0, 0:51:57
R-sq(adj) = 12,2%
R"sq = 13,O7.
ACF of the residuals "CS".
--1,0 -0,B -O,6
·to
1.
2
3
11
5
6
7
8
9
10
11
12
13
14
15
16
1i'
18
1 ~'
20
21
22
2~
24
.,~
","_.J
26
2i'
28
')<'
~,
30
--0, O01
"0,00.S
- 0, 0~(;,
"0.025
-0, 02'1
"0,038
- 0. 01/.1
0,026
--0,043
13, 0/9
0,033
0,0()3
--0,012
''0,001
--0, O34
0.025
0,0:':.i'
"O,00'<'
--0, 009
0, 04:5
-O, 001
"0,1310
- 0, 005
0;068
- 0, 027
0, 038·
-0,0'13
0,075
O,020
0,0.33
w_ • • • • • • • : • • • • , • • • • • • • • : • • •
--0,2
-~,4
w
_
w.}.
w'"
_.-,
0,0
to _ -,-_.
O , ')
X
X
-X
XX
XX
XX
X
XX
XX
XXX
XX
XXX
X
X
XX
XX
XX
X
X
XX
X
X
X
XXX
XX
XX
XX
XXX
XX
XX
0,4
~
"j_, _ ..•• _ ••• ,. _
w
0,6
• • • • • : ••••••••••••
I' _
0,B
1.0
w • • • • • • • : • • • • _ _ _ • __ ,_
189
Fig(5-8)
Multiple regression procedure of the fitted model
of the daily accidents "C2" in Riyadh area after
removing ~ and X
and the daily effect.
t-2
"'0
1ag cl. c2--c7
I'D I:: ) 1''''g1' cl 5 <:2 <:1.1--- c7;
SLI8C;} residlJal cO;
Sl.Il:C)
..
n(Jc)~:;·ta
fhe regression equation is
=- 0.120 C2 <- 0. HI5 (A <- 0.116 C5 <- 0.
Cj
102 cases 1.lsed 6 cases contain
Predictor
Noconstant
C::.'
C'1
C5
C6
Cl'
Stdev
0.11<;'81
0. HJ4~2
0. 11570
0.0')/172
0. 163~'<
1il.0371il'l
B. 13~6D
0.03728
0.11:37'11
0.0:f>/27
0.164 C7
values
~isng
Coef
C6 -c
QI~'17
too'ratio
2.04
3.10
2,~3
4.'10
s = 3.413
ACF of the residuals "C8".
--1.0 '-0.8 --13.6 '-0.'1 '-0.2
.:.0 .... '.... l.o
:I.
2
3
4
--0.0135
c-
--0,
OJ
6
7
3
<;'
113
11
12
13
111
15
16
17
13
1<;'
213
.., -~i
")
..,
.:...:..
..,",
.J1'MU
2'1
2~
'H
~'"
0.025
--0.0137
--0. 02,S
0.0
B.'!
X
XX
X
XX
XX
02~
--B. 039
XX
·-0. 01G
13.0.32
--0. 0 l l:f>
13.083
XX
0.~1
13.0'72
'-0. 011
0.1304
"0,
13.2
0~2
0.026
13.0:'G
··0, 01il3
--0.00G
0. 134'1
-(~
001
--0.1306
--0 .. 130G
13.1369
---0. 02G
13.043
.
27
0.4~
28
0.1378
2~'
0.022
313
13.033
0.6
13.8
1.0
......•... : •. _, ........ : .. ,' ....... :.: -, ....... : .•.•••• ,' .. : .. _ .•..... j ••.•...•.••.•• : ... _ ....... j .•...••• ··1·
X
XX
XXX
XX
XXX
X
X
XX
XX
XX
X
X
XX
X
X
X
XXX
XX
XX
XX
XXX
xx
XX
-,
190
h:lst cO
fiistograN of C8
N·· 71!J2
~ach
represents 5 obs.
*
Midpoint
Count
··213
_ . 11;,.'
..J
·10
7
31
?'I
1 liS'
1:53
1311
·-5
13
5
80
10
15
20
3q
5
S'
1
.,~
~;J
.50
MTE'
MTE.:
>
>
n~;<:c)
N* .. 6
Fig(5-B) cont.
:1<'~
*****:\o!:
***.*:1<.**:1<*:1<:1<:1<*:1<***
******************************
********************************
***************************
****************
*******
*
**
*
<:8 c80
pl.ot <:80 c8
C[;0
2
'l~*
2.0+
80+5*
?, .......
+++.:.
5+,:,+2
!iJ,
*
*2*
*
{iJ .,.
.:.++.:.
·'''H't,
t.~i'
s"('
*9:5
2
*2~
........... + .........................,.......................,.........................,................................. ·20
··10
0
10
20
30
N*
=
6
··ca
191
Fig(S-9)
SARIMA(O,1,1)X(O,1,1)7 for the daily accidents "C2"
in Riyadh area.
EstiMates at each iteration
Iteration
SSE
ParaMeters
0
156727
0.100
0. 100
1
123662
0.250
0.221
..,
100180
0.400
0. 342
3
82599
~J.
466
0.550
4
68941
0.700
0.594
5
58152
0.731
0.850
6
53829
0.806
0.922
7
51744
el. 855
0.964
B
51004
0.910
0.9B2
9
5lW13
0.917
0.979
10
50890
0. 920
0.977
:1.1
50B89
0.920
0.976
F(elative change in each (-:?st iMate less than
~
Final EstiMates of ParaMeters
T~lpe
EstiM,He
St. Dev.
MA
1
0.9203
0.0140
SMA 7
0.9764
0 .. 0072
0. 00Hl
t-ratio
65.79·
136.32
Differencing: 1 regular. 1 seasonal of order 7
No. of obs.
Original series 708. after differencing 70R)
Residuals:
SS = 50391.5 Cbackforecasts excluded)
MS =
72.2 DF = 698
Modified Box-Pierce chisquare statistic
12
. 24
Lag
36
Chisquare
1B.4CDF=10)
33.4CDF=22)
46.8CDF=34)
413
59. 8C DF=46 )
ACF of the residuals "CS".
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
+-~
:l
2
3
4
~
"
6
7
8
9
10
11
12
1.3
14
15
16
17
18
19
20
21
22
23
24
25
0.030
-0.041
0.014
0.031
0.021
0.087
-0.039
-0.013
-0.073
0.053
0.019
0.062
-0.052
-0.049
-0.076
0.003
0.032
-0:029
. -0. 056
0.010
-0.036
-0.029
-0.020
0.047
-0.049
XX
XX
X
XX
XX
XXX
XX
X
XXX
XX
X
XXX
XX
XX
XXX
X
XX
XX
XX
X
XX
XX
X
XX
XX
0.2
0.4
0.6
0.S
1.0
HistograM of C5
N = 71313
Each * represents 5 obs.
Midpoint
-213
30
Count
8
37
77
165
153
128
84
33
5
7
3
n~:;co
<:5 c50
-15
-113
'-5
a
~
.J
10
15
20
25
MTE:
MTE:
)
plo 'to
)
N*
Fig(5-9) cont.
192
=8
**
********
****************
*********************************
*******************************
**************************
*****************
*******
*
**
*
c5
c!,;j{l)
C50
2
2.0+
*
262*2 2
8887
*+++6
9+++
7++++
~).
0+
++++
+++7
++++
4+++9
+9+
-2. 0+
2652
*42
2
*
----+---------+---------+---------+---------+---------+--C5
-20
. -113
13
113
213
313
N* = 8
MTE:
)
plot
c6
<:5 c6
The predicted values of C2.
32+
*
*
C5
*
*
*
*
*
*
* *
*
*
2
2 * 22 * ** * * *
2
2*** * *2*23 32***2* *2 *
*
*
**2*** 3233 33*3 2* 322 ** 3 *
* *2
* **222**33 68522423*62 22*3*22 *3 2**
* * 2** 3**2 224 ** 424286*7226333 *3 2* 3**
*3 * **
33532465564266* 3* 33**3252 *2 2*
*2* ***2 2* 23565*62*5363865333**53*3**2332 3
* * **
* * 22 8443523234 246*43*422 ***4* *
*
* ***3 * **. 2 44222*352 * * ***3* * *
*2* ** 2 *3****22**2 24*2 * ** * *
2* *2 2* **
2
2*
** *
*
2
*
*
*
16+
13+
-16+
*
*
*
-+~C6
213.13
N* = 8
*
**
** * * *
25.13
313.13
35.13
413.13
Cl
Cl
1:1 •••
.., ...
••••
t_ •••• - • __ •••• to •
= _
_
_ _
• - - f • __ •• - t ___ e. _ i _____ of ______ t ______ t ______ •• ___ •••••••.. t- ••••••••••• - - • _ •• 0 .
u.
,..
~
~.
_
~
~
~
-
=
_
t __ • _. - • ______ t ______ • • _____ • __ • • • • • • • -_ • • • - - _ • • - .. ____
H'
_
IW
n.
eo. -- ____
_
--. V.
= po_e.
_ ------..
V.
et • • • • • • • __
_e,
Cl
. . . . . . . . . - _ •• _ • • • • -. - - . ___ e. - t __ • _.- t _. - - - - . -- -- _e' • • • - - . t __ • __ of - - - _ • • • _e. - __ • - _. ___ • ___ • -_f • • ____ • _____ of ______ • ___ • __ • ______ • • • _ ._ - f __
311
n,
)92
:1'1'
.tI.6
.tIU
421
.,,"
434
441
"".
4:5:5
"6:1
U'I
416
"DJ
.,.
..91
:'a"
:'11
.0 __ '.0 __ •.••••• - - t __ ._. - t __ • '0" • ______ • __ • ___
:518
:52:'
:'J2
22. :i'
Cl
1:1 •••
7. :it
•. at
• _ • • • • - f . - . __ . t ___ - - - . - .
ri'7
Z14
:i01
~.
_0 __ •
:i?Z
______
t ••
612
_0 __
t ______ t ______ t ______ t __ • ,_ • • • • • • • • • ______ • ______
. .,
616
623
Fig. (5 - 10)
631
631
64"
6:il
+_____ •• ______ • ______ f
,:;1
66:i
61Z
619
_____ • ___ w o w .
68'
,,;,
_____ • • • • __ •
.,...
_
•• _____ •
., ••
Time series plot of the daily injuries in Riyadh area.
:'3'
:'''6
:':'J
t ______ f
:'68
:'61
12. :5+
e.e ...
-12.5+
i _. __ •• _
•
C___ . _ ....... __ ... ____ . _..,.
7
~I
~1
28 -;5~2
C
-c __ • ~ __ ... _____ - .. - _____ .... --.- - ... -. ----+. -- ---c ------+--- ---... ------+------.. ------...------.... -----+------+------+------+------+------+------+------+------+
~9'
56
63
'8
"
B~
91
9B
IB5
112
119
126
133
148
14'
154
161
16B
115
lB2
IB9
t2.5+
....
-12.5C
c .. _._.· .. _____ ... _____ ·• ___ · __ .. ______ .. ______ .. ______ .. ______ i
IB9
196
2B3
211
2t7
224
231
23B
245
______ . -_____
251
c ______ .. ______ • ______ .. ______ +______ + __ ----+------+------+·----- ..
259
266
273
. 281
287
294
31t
sal
315
322
------c--____ +______ +______ +______ +______ .. ______ .. ______ +
329
336
343
351
357
364
311
37B
e. e~
- 12. 5_
+·----_c ___ • __ .. ______ t ______ •
37B
3B5
392
399
~86
c ______ .. ______ + ____ --+------+·-----c------.----__ .. ______ .. ___ •· __ t ______ .. _-----+------... -------------+------c-----_c ______ + ______ +------+------+------+------c
413
~21
421
434
441
448
455
462
469
476
49J
498.
497
584
511
5t8
525
532
53.
546
553
5.8
567
______
••••
-12.5+
.. - - - - -- c- ___ ••• ______ .. -- --. - .. - - - __ - .. _ - -- • - .. ---- --.. ------ .. ---- --11'- __ -
561
574
581
Table (5-11)
588
5.5
682
68.
616
623
63,
- - t - - . - - ... - - - - __ .. ______ .. ______ .. ____ • _. ______ + ______
637
644
651
658
665
672
67.
.. ______ • ______ + ______ + ______ +
686
69)
781
787
714
Time series plot of the first difference of the daily injuries in RiYadh area.
195
ACF of C33
-1.0 -0.8 -13.6 -0.4 -13.2
0.0
0.2
0.4
0.6
0.8
1.0
}-~.+
1
2
3
4
5
6
7
8
9
10
11
1"
:L3
14
15
16
17
18
19
20
21
22
23
24
.,~-
~.J
.26
27
28
2S'
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
- 0. 5313
13.1363
-,0. 1329
13.1329
- B. 1371
0.025
0.1322
13.13113
-. 0. 1329
13.034
- 0. 065
0.056
0.1329
'-13. 085
0.042
0.048
-0.088
0.091
- 0. 103
0.041
0.023
0.011
- 0.032
0.018
-0.033
0.051
-0.093
0.095
-0.1315
0.004
-0.041
0.050
- 0. 041
0.027
- 0. 048
0.070
··0. 051
0.034
- 0. 019
--0.1322
0.042
0.012
-,0.058
0.045
-0.013
-0.014
-0. 1316
0.070
-0.045
'-0.1329
Fig(5-12)
XXXXXXXXXXXXXX
XXX
XX
XX
XXX
XX
XX
X
XX
XX
XXX
XX
XX
XXX
XX
XX
XXX
XXX
XXX X
XX
XX
X
XX
)(
XX
XX
XXX
XXX
X
X
XX
XX
XX
XX
XX
XXX
XX
XX
X
XX
XX
X
XX
XX
X
X
X
XXX
XX
XX
ACF of the differenced series "0))" ut the
in Ri~adh
area.
dail~
i~ures
"C)"
196
PACi- of C33
-1.0 --0.8 ·0.6 ·-0.4 --0.2
l.
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
1S'
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
- 0. 530
-0.304
···EL 225
-0.135
- 0. 187
-0. 187
- 0. 135
-0. 080
- 0.092
-0. 051
- 0. 127
-0. 087
0.020
-0.070
- 0. 072
0.027
- 0.050
0.057
- 0.054
--0. 092
- 0. 023
0.01?
-0.003
0.000
- 0.070
0.003
-0.086
-0.061
-0.008
0.014
-0.042
0.024
-0.013
0.000
--0.035
0.002
~-'I.·
0.0
0.2
0.4
0.6
0.S
1.0
XXXXXXXXXXXXXX
XXXXXXXXX
XXXXXXX
XXX X
XXXXXX
XXXXXX
XXXX
XXX
XXX
XX
XXX X
XXX
XX
XXX
XXX
XX
XX
XX
.XX
XXX
XX
X
X
X
XXX
X
XXX
XXX
X
X
XX
XX
X
X
XX
X
Fig(5-13) : PAeF of the differenced series "e33" of the daily injuries "e3"
in Riyadh area.
197
Fig(S-14) : ARDilA(O,O,1) for the differenced serieS "0)3"
of the daiJ.y injuries "0)".· in Riyadh area.
Est. i .... at.es at each iteration
Iteration
SSE
F'ara"',eters
15205.2
0.100
0.037
0
13302.3
0. 044
1
0.250
0.018
11848.5
0.400
2
0.550
0.004
3
10709.7
-0.002
0.700
4
9792.0
-·0. 003
9047.6
0.850
5
-0.001
8700.7
0. 954
6
0.001
7
8697.8
0.960
0.001
8
8697.8
0.960
Relative change in each estil".ate less than 0.0010
Final Est i~at.es
T~lpe
MA
1
Cemst.ant
Mean
No.
of Parai1eters
Estif".ate
St. Dev.
0.9600
0.0027
0.000759
0.006537
0.000759
0.006537
of obs.:
t.-·ratio
357.54
0.12
707
ss
= 8659.90
12.28
MS =
f~esidual:
(backforecasts excluded)
DF = 705
Modified Box-Pierce chisquare statistic
12
24
Lag
36
10.2(DF=11)
26.0(DF=23)
40.3(DF=35)
Chisquare
48
47. 0( DF=47 )
ACF of C5 (residuaJ.s).
-1.0 -0.8 ··0.6 ·-0.4 ·-0.2
.- 0. 010
1
0.052
2
3 .- 0. 007
4 -0.007
5 ·-0. 067
0.013
6
0.040
7
0.026
8
9 ·0. 009
10
0.014
11 ·0.032
0.056
12·
13
0.030
14
-0.054
0.027
15
0.031
16
17 -0.069
0.014
18
19 -0.093
20
0.009
21
0.032
22
0.008
23 -0.036
24
-0.017
25 ---0.041
26
0.009
·0.
045
27
0.093
28
0. 034
29
0.011
30
~-+'}.
l
0.0
X
XX
X
X
XXX
X
XX
XX
X
X
XX
XX
XX
XX
XX
XX
XXX
X
XXX
X
XX
X
XX
X
XX
X
XX
XXX
XX
X
0.2
0.4
0.6
0.8
1.0
198
Fig(5-14) cont.
HistograM of C5
N = 707
Each * represents 5 obs.
Count
7
28
115
138
146
144
70
34
18
5
1
1
Midpoint
··8
-6
-4
-·2
0
2
4
6
8
l.0
12
lA
MTE:
> plot
**
******
***********************
****************************
******************************
*****************************
**************
*******
****
*
*
*
c5 c6 (predicted values).
14.0-1
*
cs
*
*
*
*
* *
*
0.0-1
*
2
* 2*
3
*
*
*3* 2 * 2*2 * *
* * *2 2 2 3* 3 **2 **
3 2 *2*4*** 233*3 4**4** **
33*2****234*46*638343 *645333**
*
7.IH
2 222*245333563*3645*454 4*222 22
*
*
*
*
2 22** 443+555*4*6838452 62*4 2 *
*
2 *4*52743+36437245*53422*2
***
* 2 3 2* *22433323435*45+22626 *2*
* *
* 3262333764749*2422433*
***
** 2 *2 3 ****2**** 2*
22
*2
*
-7. 0
**** **
*
~
*
*2
*
*
**
2*
*
------+----------1---------+---------+---------+---------+C6
-12.0
-8.0
-4.0
0.0
4.0
8.0
MT8
> plot
c50 cS
(C50
normal scores of the residuals "C5" ).
C50
2.
3* 3
**
e to
42432
5-1376
4~962
6-1 -1'-1
.t-++ ... ~
+-1-1-1
0.0-1
~9
++-1"
........ 1-
*9+
2?4
'-2.0+
*2**2
2
*
-I·~
-8.13
-4.13
_____ _I-i·.~
13.13
4.0
8.13
-+C5
12.0
*
199
Fig(5-1,5) : I,.RD.lA (O,Cl, 1) for thA differenaed ser1es "011" nf the
a!l.11y injuries
"e)" in Riyadh area after removing the
constant.
EstiMates at each iteration
I ter at ion
SSE
F'aral",eters
0
15196.8
0.100
1
13298.8
0.250
2
11847.3
0.4013
3
10709.5
0.550
4
9792. 1
0. 700
9047.6
5
0.850
8700.2
6
0.954
8698.0
7
0.960
8698.0
8
0. 96~J
F~elativ
change in each est il",ate less than
Final EstiMates of ParaMeters
Type
Esth;ate
St. Dev.
MA
1
0.9599
13.13011
No.
of obs.:
0.
~10
t-'ratio
866.68
707
ss
= 8660.33
MS =
12.27
F~esidual:
(backforecasts excluded)
DF = 706
Modified Box-Pierce chisquare statistic
Lag
36
12 24
Chisquare
10.2(DF=11)
26.0(DF=23)
40. 4( DF=35 )
ACr-
0
f
C5 ( residuals ).
-1.0 -0.8 '-0.6 '-0.4 ·-0.2
0.0
~-}.+
1
2
3
4
5
6
7
8
9
HI
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
48
47. 1( DF=47 )
·-0.1310
0.052
·0.007
-0. 1307
-'-0.1367
0.013
0.13413
0.026
- 0. 009
0.014
- 0. 032
0.056
0.030
-0.1354
0.027
13.1331
- 0. 069
0.014
- 0. 1393
0.009
0.032
0.008
- 0. 036
-0.017
--0. 1341
0.009
- 0. 045
0.2
0.4
13.6
0.8
1.0
-_.}
X
XX
X
X
XXX
X
XX
XX
X
X
XX
XX
XX
XX
XX
XX
XXX
X
XXX
X
XX
X
XX
X
XX
X
XX
200
HistograM of C5
N = 707
Each * represents 5 obs.
Count
7
27
114
138
146
146
69
35
17
6
1
1
Midpoint
--8
-6.
-4
-2
0
2
4
6
8
10
12
1.4
N* = 1
Fig(S-1S) cont.
**
******
***********************
****************************
******************************
******************************
**************
*******
****
**
*
*
plot c5 ,:6
(C6
the predicted values).
*
14.0'1'
******
C5
7. 0
2
*
* 2*
3
*
22** 2 * 2*2 * *
*
*
* * *2 2 2 2* 3 **2 **
3 2 *2*4*** 242*3.4**5** **
*
33*3***2*34*55*728343**645323**
. *
* * 2 222 245424562*3645*444*3*222 22
22
2 22** 443+564*4*8647543*5223 2 *
*
* * ** 23*6*743+365382352334322*
***
* 2
* 2 3 2* *22523324354*45+*44*7 *2* *
*
*
* 3262342754649*2422423*
***
* * 2 *2 3 ****2*2 * 2*
*
*
*
**
2*
2
*
*
~
*
*
*
0.0+
*
-7. 0
~
*
*
------0---------0------7--+---------+---------+---------+C6
-12.0
-8.0
-4.0
0.0
4.0
8.0
N* = 1
MTB > nsco c5 c50
MTB > plot c50 c5
C50
22 2*
**
*
33432
2.0t-
50·376
2"9).53
4 ......
~
I'+~
~
+-1 -(+
}ot-+++
0.0+
..........
+·H·
*8---2.0+
285
3**2
2
*
__ -( ___ . _______ -( ______ . ___ -( ____ · _____ -( _________ i _______ --+----C5
-8.0
N* = 1
-4.0
0.0
4.0
8.0
12.0
co
7.BIH
1.~B
e. ee ..·
t--
----t- ---- -+ •• - - ••
8
7.
7
14
t • _____ t-- • ___ ._ .---- .------ .----- ' •• ----- . - - - - - - . - - - ___ • - _____ • ______ • ______ • ______ • ______ • ______ • ______ • ___ -. · t . ' . - - - .... _ • • .
21
20
J:i
42
49
'!i6
63
78
77
84
91
90
19S
112
119
126
133
148
t-_· -- - .. - _. -. - t- • - ___
147
1:;4
161
t ______ • - - - - - - . - - - - - - .
168
17:5
la:!
199
aet
1. :;81
B.
ee. t . , . ---i . ____ - t , ' _____ i
109
196
leJ
2U
__ • ___ .. - - - . _ ... - _ • • - - . - - - - - - . - - - - - - . - - - - - - . - •. "
217
224
231
2J8
245
2:52
• 'I"
2:59
- - - - - ..... ___ t --.--- of - - - - - - t ______ • ______ • ______ ._ - - - - - •• _ •• _ • • - - - - - - ... - _ . . . . . ' •• - - - i ______ .. _. ____ • ______ • ______ .. ____
266
273
288
20]
294
JBt
lea
31:5
322
329
JJ6
J43
JSS
3::;7
J~4
J7\
po.
370
N
o
7.80+
8,811h
", . . ___ • ______ •. _____ i ______ .. ______ t_ ----
378
38"
392
399
4a,
413
-t------+--- ---+------t-- ----i--- -. -t- -----+---. -- t-·· -. -+- -----. ------t------t--____ t·· -- _-+---. __ . _____
4::!8
427
434
441
448
45'
462
469
476
403
498
497
!i94
511
518
7. ea ...
e.0a+
~67
of - •• - - -
~74
f- -- - -- of - - Sal
- - - f -. - - - - .. ___ - - _of - - - - - -
58e
:;95
Fig(5-16)
,a2
f -. ----f- -----f------ .. ----. -+.: __ --t----.
609
616
6::!l
63a
617
644
- i ______
651
+____ --t------t------.
65e
665
672
'79-~;6·e=
t -
Time series plot of the daily.fatalities in Riyadh area.
t"
!i~:;
-of ___ • __
to __
532
-;~
-
-
-
-
202
o'f C4
,~cr-
"1,121 "121,8 "121,6 "121,4 "121,2
'I-~
1
2
3
4
5
,s
7
3
9
1121
11
12
13
14
15
1,s
17
13
19
20
21
22
23
24
25
2,s
27
28
2<;'
30
31
32
33
34
35
3,s
37
38
3'7
40
41
42
43
44
'15
4,s
47
43
49
5O
H'_
~
..
-
~'-
-I- - - --t-- .. -
"121,017
eJ,05,s
"121,1211212
-121,1214'7
121,064
"121,1211216
121,039
eJ,eJ4,s
,,0, 1211214
0,0121121
. (3,062
0,013
"0.1211218
0, (,-)23
,,0, 020
0,06,s
0,12118
,121, 12114
"0, 1211211
0,12177
0,12128
0,12119
0, (114
0,01214
121,2
121,4
121,6
121,8
X
XX
X
XX
XXX
X
XX
XX
X
X
XXX
X
X
XX
XX
XXX
X
X
X
XXX
XX
X
X
X
XX
X
XX
X
X
XX
XX
XX
XXX
X
X
XXX
X
XX
X
XX
X
XX
X
XX
XXX
X
X
XX.
X
XX
0.022
"121,1211211
0, (344
0,01'7
"0,01121
121,12131
- 0. 02<7
0,12144
0,12176
"121,12112
0,018
0.067
0,12114
121,12124
121,014
121,041
"0,020
0,020
"0, 01212
"'0,022
"0, 081
"0, 1212121
0,01217
0, 035
0,1211210
0,031
Fig(5-17)
121,121
- } ----f- -- - -Jo-- .. _ol·_ .. _--J------l-. __ .-
. ACF of the
daily fatal.ities "C4" in Riyadh area.
1,121
_.~
203
PACF 'of C4
--1.13 -13.8 -,13.6 "13.4 --0.2
~
1
'-0.017
2
0. 05\S
3
-,0.0131
4
5
--0. 052
,
"
7
a
9
113
11
12
13
14
15
16
17
18
19
20
21
....
"V)
..:..
23
24
25
26
27
28
29
30
31
32
"')3
34
35
36
37
38
3'7
40
41
42
43
44
45
46
47
48
49
50
w
~
13. 1363
0.0131
0.032
13.046
.- 13.-0131
---13.13139
--13.1358
0.017
-(~.
006
0. 024
-"0.027
0.070
0.020
---0.014
---0.0135
0.039
0.022
0.002
0. 1314
0.1304
0. 015
-0.1304
0.049
0.0113
--el. 016
0.023
-13. 010
0.033
0.076
'-0.013
0.004
0.070
0.1310
0.013
0. 017
13.032
- 0.039
13.1315
"0.0132
--0. 023
--0. 097
-0.020
0.011
0.029
--13.016
0.031
Fig(5-18)
_~
M'l- M _ ...... J- __ ... _
13.0
13.2
13.4
t·: .. - .. -- ,.. "' .. - -.}- - .. - .. l· - - - ..
~
0.6
13.8
X
XX
X
XX
XXX
X
XX
XX
X
X
XX
X
X
XX
XX
XXX
X
X
X
XXX
XX
X
X
X
X
X
XX
X
X
XX
X
XX
XXX
X
X
XXX
X
X
X
XX
XX
X
X
XX
XXX
X
X
XX
X
XX
PACF of the daily fatalities "C4"
1.0
- ---.- 1- .•.- .. -I- ".- ., -.,.
!n Riyadh area.
Monthly fatalities in Saudi Arabia
Monthly injuries in Saudi Arabia
Monthly accidents in Saudi Arabia
2500
2600
21500
2.00
2.00
2200
2200
2000
2000
1800
400
350
~
C
G
:2
u
u
D
1500
~
11500
~
c
300
,
:5
"
:f:
]
·0
11500
250
-ll
,.00
200
N
..,.
0
1200
150
100
600'+----.----r---,----.----r---,----.60
80
100
120
uo
40
20
o
400+----.---,r---.----r---.----.----r60
80
100
120
wo
40
20
o
months
months
Fig(5-19)
50+----.---.---,r---.---,----.---.-60
80
100
120
wo
40
20
o
Monthly accidents, injuries, and fatalities in
Saudi Arabia.
months
205
st
Fig(5-20) : Time series plot of the 1
difference of the monthly
accidents "C2" in Saudi Arabia.
250+
0+
--250+
+-----------+-----------+-----------+-----------+-----------+
o
12
24
36
48
60
C21
250+
Il:
0+
-250+
+-----------+-----------+-----------+-----------+-----------+
60
84
72
C21
250+
\
0+
-250+
+-----------+-----------+
120
N* = 1
132
144
96
108
120
206
ACF of C21
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
1
2
3
4
5
6
7
8
9
10
:1.1
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
XXX XX
XXXXXX
XX
XXX
XX
XX
XX
XX
XX
XX
XXX
XXX
XXX
XX
XXXX
XXX
XXX
XXXX
XX
XXXX
XXXXXXXX
XXXXX
XXXX
. XXXX
XXX
XX
X
XXX
X
XXXX
X
XX
XX
XXXX
XXXX
XXX
X
XXX
XXX
XX
XX
XXXXX
XXX
XX
XXX
XXXX
X
XXX X
XX
X
-0. 175
-0. 183
0.054
-0.075
-0.029
-0.047
-0.041
-0.052
0.026
-0.033
0.065
0.083
-0.095
-0.049
0.115
-0.070
-0.063
0. 124
0.033
-0. 110
0. 269
-0. 168
":'0. 122
0. 124
-0.070
0.031
0.007
-0.077
-0.001
0. 109
-0.008
0.043
0.027
-0. 109
-0.114
0.068
0.017
'-0.098
0.080
-0.035
0.023
0. 157
-0. 100
-0.035
0.086
-0. 136
0.000.
0. 139
-0.038
-0.000
Fig(5-21 )
I
ACF of the 'differenced series "C21" of the monthly
accidents "C2" in Saudi Arabia.
207
PACF of C21
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
3940
41
42
43
44
45
46
47
48
49
50
-0. 175
-0.220
-0.026
-0.119
-0.068
-0. 116
-0. 106
-0. 145
-0.072
-0. 127
-0.013
0.028
-0.091
-0. 117
0.025
-0.092
-0. 101
0.040
0.053
-0.089
0.278
-0.093
-0.071
0.051
0.001
0.041
0.044
-0.034
-0.021
0.046
0.054
0.095
0.046
0.000
-0. 110
-0.082
0.009
-0. 103
-0.041
-0. 108
0.005
0.002
-0.041
-0.042
-0.041
-0.113
-0.055
0.069
0.032
0.045
Fig(5-22)
XXXXX
XXXXXXX
XX
XXX X
XXX
XXXX
XXX X
XXXXX
XXX
XXXX
X
XX
XXX
XXX X
XX
XXX
XXXX
XX
XX
XXX
XXXXXXXX
XXX
XXX
XX
X
XX
XX
XX
XX
XX
XX
XXX
XX
X
XXXX
XXX
X
XXXX
XX
XXXX
X
X
XX
XX
XX
XXX X
XX
XXX
XX
XX
..
. PACF of the differenced series· "C21"
accidents "C2" in Saudi Arabia.
of the monthly
208
ACF of C2
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
1
2
3
4
5
6
7
8
9
H)
11
12
13
14
0.943
0.890
0.853
0.811
0.769
0.739
0.707
0.684
0.670
0.662
0.648
0.627
0.597
0.578
15
8.562
16
17
18
19
20
21
22
23
24
0.538
0.514
0.497
0.477
25
26
27
28
0.452
0.439
0.400
0.372
0.356
0.329
0.306
0.289
0.270
29
0.254
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
0.238
0.218
0.200
0. 176
0. 156
0. 147
0. 143
0. 130
0. 117
0.114
0.110
0.107
0. 107
0.088
0.061
0.043
0.021
0.013
0.005
-0.010
-0.017
Fig(5-23)
XXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXX
XXXXXXXXXXXXXXX
XXXXXXXXXXXXXX
XXXXXXXXXXXXXX
XXXXXXXXXXXXX
XXXXXXXXXXXXX
XXXXXXXXXXXX
XXXXXXXXXXXX
XXXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXXX
XXXXXXXXX
XXXXXXXX
XXX Xxx XX
XXXXXXX
XXXXXXX
XXXXXX
XXXXXX
XXXXX
XXXXX
XXXXX
XXXXX
XXXX
XXX X
XXX X
XXXX
XXX X
XXX X
XXX
XXX
XX
XX
X
X
X
X
ACF of the monthly accidents "C2" in Saudi Arabia.
209
.Fig(5-24) i ARIMA(2,' ,0) for the monthly aooidents "C2"
in Saudi Arabia.
ariMa 2, 1,0 c2 <:5 c6;
EstiMates at each iteration
ParaMeters
I terat ion
SSE
0. 10(3
2598386
0. 100
0
-0.050
2326567
-0.047
1
-0.193
-0.200
2
2223334
2222185
-0.209
-0.217
3
2222181
-0.209
-0.218
4
-0. 218
5
2222181
-0.209
Relative change in each estiMate less than
F ina 1 EstiMates of ParaMeters
St. oev.
Type
EstiMate
0.0836
AR
1
-0.2095
0.0836
AR
2
-0.2183
0.0010
t-rat i(J
-2,51
-2.61
oifferencing: 1 regular difference
No. of obs.:
Original series 144, after differencing 143
Residuals:
SS = 2221684 (backforecasts excluded)
MS =
15757 OF = 141
Modified Box-Pierce chisquare statistic
12
24
36
Lag
42.7(oF=34)
8. 9( of=10)
30. 4( of=22 )
Chisquare
48
57. 7( of=46 )
ACF of C5 (residuals)
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
-0.021
-0.042
-0.058
-0. 138
-0.059
-0. 100
-0.072
-0.069
0.027
-0.014
0.066
0.071
-0.060
-0.052
0.060
-0.er.58
-0.029
0. 104
0.098
-0.059
XX
XX
XX
XXXX
XX
XXXX
XXX
XXX
XX
X
XXX
XXX
XXX
XX
XXX
XX
XX
XXX X
XXX
XX
210
Fig(5-24) cont.
Time series plot of the residuals.
250+
0+
-250+
+-----------+-----------+-----------+-----------+-----------+
o
12
24
36
48
60
250+
0+
-250+
+-----------+-----------+-----------+-----------+-----------+
60
72
84
250+
0+
-250+
+-----------+-----------+
120
132
144
96
108
120
. 211
Fig(5-24) cont.
Midpoint Count
1 * Histogram of C5 N N=14J
-350
2 **
-300
1 *
-250
6 ******
-200
5 *****
-:L50
16
-100
-50
23 ****************
***********************
20 ********************
0
29 *****************************
50
16 ****************
100
150
12 ************
5 *****
200
2 **
250
3 ***
3130
2 **
3513
MTB > nsco c5 c50
MTB > plot c50 c5
C50
2.0+
*546
795
*858*
5466
0.13+
33333* *
*2
*
**
5+*
*325*
-2.0+
2
**
--------+---------+---------+---------+---------+--------cs
-3013
MTB
C5
>
plot c5 c6
-1513
(C6
0
150
300
The predicted values).
*
*
*
*
*
*
2
*
*
4
2
*
*
* * * *
- ** * * * ** ***
* * *2 ** *
*3
3**4**2
* *
***
* 2*3
0+
2
23
*
** ** 2
*** *
** **
* *
* 2***2** * *
*
*
3*
*
* *
*
* * * **
**
*
*
*
*
* * ***
-250+
* *
250+
*
"*.
*
* *
*
*
**
*
--------+---------+---------+---------+---------+--------C6
1050
14013
1750
2100
2450
212
ACF of C3
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
+-~
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
0.884
0.843
0.792
0.748
0.708
0.691
0.663
0.681
0.669
0.676·
0.677
0.696
0.640
0.603
0.565
0.539
0.503
0.482
0.467
0.467
0.460
0.450
0.449
0.473
0.416
0.374
0.337
0.303
0.274
0.254
0.231
0.243
0.228
0.235
0.248
36
0.269
37
0.232
38
0.186
39
0.150
40
0. 136
41
0.097
42
0.083
43 - 0.067
44
0.064
45
0.067·
46
0.063
47
0.066
48
0.080
49
0.048
50
0.015
35
Fig(5-25)
XXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXX
XXXXXXXXXXXXXX
XXXXXXXXXXXXXX
XXXXXXXXXXXXX
XXXXXXXXXXXXX
XXXXXXXXXXXXX
XXXXXXXXXXXXX
XXXXXXXXXXXX
XXXXXXXXXXXX
XXXXXXXXXXXXX
XXXXXXXXXXX
XXXXXXXXXX
XXXXXXXXX
XXXXXXXXX
XXXXXXXX
XXXXXXX
XXXXXXX
XXXXXXX
XXXXXXX
XXXXXXX
XXXXXXX
XXXXXXXX
XXXXXXX
XXXXXX
XXXXX
XXXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XX
X
. ACF of the monthly injuries
"C3".in Saudi Arabia •
1.0
213
F'ACF
of C3
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
0.884
0.279
0.037
0.019
0.016
0. 109
0.016
0.217
0.010
0.080
0.059
0.138
-0.264
-0. 131
0.001
0.025
-0.046
-0.031
0.055
-0.020
0.033
-0.050
0.046
0.151
-0.215
-0. 126
-0.030
0.007
-0.005
0.002
-0.026
0.048
-0.022
0.090
0. 077
0.043
-0.075
-0. 166
'-0.011
0.080
-0.064
-0.001
-0.007
-0.057
0.050
-0.007
-0.003
':'0.034
0.000
-0.007
Fig(5:'26)
XXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXX
XX
X
X
XXXX
X
XXXXXX
X
XXX
XX
XXXX
XXXXXXXX
XXXX
X
XX
XX
XX
XX
XX
XX
XX
XX
XXXXX
XXXXXX
XXX X
XX
X
X
X
XX
XX
XX
XXX
XXX
XX
XXX
XXXXX
X
XXX
XXX
X
X
XX
XX
X
X
XX
X
X
PACF of the monthl.y injuries "C)" .1n Saudi Arabia.
214
Fig(5-27)
Time series plot of the differenced series "C)1" of the
monthly inj=ies "C)" in Saudi Arabia.
500+
C31
0+
-500+
-1000+
+-----------+-----------+-----------+-----------+-----------+
o
12
24
36
48
60
500+
C31
0+
-500+
-1000+
+-----------+-----------+-----------+-----------+-----------+
60
72
84
500+
C31
0+
-500+
-1000+
+-----------+-----------+
12a
132
144
96
108
120
215
ACF of C31
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
-0.378
0.038
-0.013
-0.019
-0.062
0.007
-0.251
0. 195
-0.086
-0.032
-0.061
0.295
23
-0.036
-0.011
-0.045
0.088
-0.038
-0.022
-0. 101
0.017
-0.008
-0.086
-0.087
24
0.272
25
26
27
28
0.024
0.005
-0.039
-0.003
-0.051
0.012
-0. 133
0. 102
-0.080
-0.030
-0.028
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
0.221
0.030
-0.045
-0.062
0.114
-0. 130
0.073
-0. 124
0.018
0.020
-0.096
0.004
0. 144
0.018
0.004
Fig(5-28)
XXXXXXXXXX
XX
X
X
XXX
X
XXXXXXX
XXX XXX
XXX
XX
XXX
XXXXXXXX
XX
X
XX
XXX
XX
XX
XXXX
X
X
XXX
XXX
XXXXXXXX
XX
X
XX
X
XX
X
XXXX
XXX X
XXX
XX
XX
XXXXXXX
XX
XX
XXX
XXXX
XXXX
XXX
XXXX
X
XX
XXX
X
XXXXX
X
X
-'AeF of the difference seri-es "e31 " of the monthly
injuries "e3" in Saudi Arabia.
216
th
difference of
Fig(5-29) : Time series plot of the 12
the monthly injuries "e)" 1n Saudi Arabia.
C42
~50+
IN
0+
-500000+
+-----------+-----------+-----------+-----------+-----------+
o
12
24
36
48
60
C42
500000+
-500000+
+-----------+-----------+-----------+-----------+-----------+
60
72
84
96
108
120
C42
500000+
I
!
.: tfi \ ~ lvY\
.;
-500000+
+-----------+-----------+
120
132
144
217
ACF of C42
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
1
2
3
4
5
6
7
8
9
10
-0.923
0.738
-0.525
0.360
-0.274
0.252
-0.258
11
-0.247
0.239
-0. 225
0.203
-0. 175
0. 140
-0.099
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
.50
0.265
-0.261
0. 254
0.055
-0.015
-0.004
-0.005
0.041
-0.085
0.117
-0. 125
0.112
-0.095
0.089
-0.1000. 123
-0. 147
0. 162
-0. 166
0.161
-0. 157
0. 159
-0. 173
0.201
-0.236
0.265
-0.271
0.249
-0.2B2
0. 148
-0. 102
0.070
-0.051
0.033
-8.009
-8.021-
Fig(5-)O)
XXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXX
XXXXXXXXXX
XXXXXXXX
XXXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXX
XXXXXXX
XXXXXXX
XXXXXXX
XXXXXXX
XXXXXX
XXXXX
XXXXX
XXX
-,
XX
X
X
X
xx
XXX
. XXXX
XXXX
XXXX
XXX
XXX
XXXX
XXXX
XXXXX
XXXXX
XXXXX
XXXXX
XXX XX
XXXXX
XXXXX
XXX XXX
XXXXXXX
XXXXXXXX
XXXXXXXX
XXXXXXX
XXXXXX
XXXXX
XXXX
XXX
XX
XX
X
XX
ACF of the 12th difference of the monthly
injuries "C)" _ in Saudi Arabia.
218
ACF of C43
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
XXXXXXXXXXXXXXXXXXXXXXXX
-0.930
0.757
-0.554
0.387
-0.292
X~
XXXXXXXXXXXXXXX
XXXXXXXXXXX
XXXXXXXX
XXXXXXX
XXXXXXX
XXXXXXXX
XXXXXXXX
XXXXXXXX
XXXXXXX
XXXXXXX
XXXXXXX
XXXXXX
XXXXX
XXXX
XXX
XX
0.259
-0.260
0.266
-0.267
0.262
-0.256
0.247
-0.233
0.209
-0.177
0. 138
-0. 092
0.046
-0 .. 011
-0.003
-0.010
X
X
X
PACF of C43
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
-0.930
-0.783
-0.504
0.213
0. 134
-0.089
-0.091
0.125
-0.041
-0.034
0.034
0.004
-0.033
-0.005
0.077
-0.098
0.009
0.080
-0.073
-0.000
0.013
Pig(5-31)
XXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXX
XXXXXX
,XXXX
XXX
XXX
XXXX
XX
XX
XX
X
XX
X
XXX
XXX
X
XXX
XXX
X
X
ACP and PACP of the eeasonal and nonseasonal differece of the
monthly injuries "C3" in Saudi Arabia.
219
Fig(5-)2) :'ARIMA(2,1,O)X(O,1,1)12 for the monthly injuries "0)"
in Saudi Arabia.
ariMa 2, 1, la 0, 1, 1 12 c3 c5 c6
EstiMates at each iteration
I terat ion
SSE
ParaMeters
0
5153215
0.100
0. 100
4061180
1
-0.050
0. 035
2
3229126
-0.197
-0.030
2736930
3
-0.314
-0.084
2438331
-0.421
-0. 133
4
5
2293990
-0.534
-0. 179
6
2288329
-0.538
-0. 170
2287217
7
-0.536
-0. 167
-0.535
8
2286984
-0. 166
9
2286943
-0.534
-0. 166
10
2286941
-0.534
-0. 165
11
2286941
-0.534
-0. 165
Relative change in each estiMate less than
Final EstiMates of ParaMeters
Type
EstiMate
St. Dev.
AR
1
-::.eL5341
j1k08Z2,
2
-0. 1654
0.8873
AR
SMA 12
0.8462
0.0729
0. 100
0.214
0.364
0.514
0.664
0.814
0.833
0.840
0.844
0.845
0.846
0.846
0.0010
t-ratio
-6.12
-1. 89
11.62
Differenci"ng: 1 regular, 1 seasonal of order 12
No. of obs.:
Original series 144, after differencing 131
Residuals:
SS = 2217709 Cbackforecasts excluded)
MS =
17326 OF = 128
Modified Box-Pierce chisquare statistic
Lag
12
24
36
Chisquare
16.4CDF= 9)
21.6CDF=21)
37. BC DF=33 )
48
46. 4C DF=45 )
220
ACF of C5 ( residuals )
Fig ( 5- 32) cant.
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
0.005
0.013
-0.056
-0. 157
-0.065
-0. 138
-0.216
0.108
-0.012
0.021
0.043
-0.069
-0.001
0.053
0.041
0. 086
0.060
-0.019
-0.003
-0.057
-0.014
-0.089
-0.079
0.016
0.116
0.082
-0.022
-0.151
-0.119
-0.061
-0.008
0.084
-0.094
0.076
0.074
0.076
0.081
-0.069
-0.065
0.034
-0. 105
0.012
-0.026
-0.024
0.077
0.027
0.024
-0.087"
0.028
0.024
X
X
XX
XXXXX
XXX
XXXX
XXXXXX
XXXX
X
XX
XX
XXX
X
XX
XX
XXX
XX
X
X
XX
X
XXX
XXX
X
XXXX
XXX
XX
XXXXX
XXXX
XXX
X
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XXX
XX
XXXX
X
XX
XX
XXX
XX
XX
XXX
XX
XX
221
Fig(5-)2) cont.:Time series plot of the residuals.
300+
B
2
7
4
1 3
2
34 6
0+
AB
5
5
4
1
9 A
23 56 8
0
Bl
7
89
4
0A
56
6
8
7
3
89
7
2
90
B
A
-300+
+-----------+-----------+-----------+-----------+-----------+
o
12
24
36
48
60
C5
A
B
300+
-
o
1
8
A
90
9
45
0+
6
23
8
7
5
1
478
3 56
A 1
6
90
2 4
0
B
B
3 5 7
6
78
6
7 9
2
9
1 3
A
8 0A
23
5
B
2
-300+
4
B
1
4
+-----------+-----------+-----------+-----------+-----------+
60
72
84
96
108
120
C5
300+
9
:a
0+
2
0
6
0
56
B
9
8
5
7
8
B
A 1
A
34
-
7
1 34
-300+
+-----------+-----------+
133
222
Fig(5-32)
Midpoint Count
Histogram of C5 Na13.1
4 ****
-300
12 ************
-200
28 ****************************
-100
0
38 **************************************
100
36 ************************************
10 **********
200
300
1
1 *
400
1 *
500
*
MTB plot c5 c6 (C6 The predicted values).
500+
*
C5
*
cont.
)
*
*
**
*
*
2
2 *
2
*
*
* *4
* * * ***
* * ** * *2*
22 *
*
**
**
*
*
**
* * ** *
0+
2* * 3 2 2 2 * * ***3
*
*
*
*
* *** 2 2* *
* *** *
* *
* * * ** * * * ***
** *
*
* * * **
*
*
**
* *
-250+
* **
*
*
*
--+---------+---------+---------+---------+---------+----C6
600
900
1200
1500
1800
2100
2513+
MTB ) nsco c5 c50
MTB ) plot c50 c5
C50
2.0+
22*
0.0+
-2.0+
* *
*433
*2 **
2*
35*+
5343
4223
464*
3574
3882
** *
.*
*
----+---------+---------+---------+---------+---------+--C5
-300
-150
0
150
300
450
223
ACF of C4
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
1
2
3
4
5
6
-7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
0.698
0.624
0.582
121.524
0.442
0.428
0.419
0.472
0.489
0.478
0.491
0.643
0.495
0.419
0.390
0.348
0.273
0.265
0.217
0.268
0.307
0.293
0. 334
O,452
0.333
0.284
0.236
0. 195
0. 135
0. 107
0.073
0.117
0. 171
0.155
0.187
0.349
0.212
0. 150
0.119
0.097
0.026
-0.025
-0.051
-0.011
0.028
0.052
0.0420.175
0.079
0.030
Fig(5-33)
XXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXX
XXXXXXXXXXXXXX
XXXXXXXXXXXX
XXXXXXXXXXXX
XXXXXXXXXXX
XXXXXXXXXXXXX
XXXXXXXXXXXXX
XXXXXXXXXXXXX
XXXXXXXXXXXXX
XXXXXXXXXXXXXXXXX
XXXXXXXXXXXXX
XXXXXXXXXXX
XXXXXXXXXXX
XXXXXXXXXX
XXXXXXXX
XXXXXXXX
XXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXX
XXXXXXXXX
·XXXXXXXXXXXX
XXXXXXXXX
XXXXXXXX
XXXXXXX
XXXXXX
XXXX
XXXX
XXX
. XXXX
XXXXX
XXXXX
XXXXXX
XXXXXXXXXX
XXX XXX
XXXXX
XXXX
XXX
XX
XX
XX
X
XX
XX
XX
XXXXX
XXX
XX
-.
ACP of the monthly fatalities "C4" in Saudi Arabia.
224
F'ACF of C4
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
0.698
0.265
0. 160
0.053
-0.048
0.067
0.082
0.208
0. 128
0.025
0.053
0.391
-0.232
-0. 170
-0.061
-0.040
-0.056
0.005
-0. 121
0.026
0.089
0.020
0.132
0.114
-0. 152
-0.005
-0.068
-0.042
-0.006
-0.098
-0.015
0.031
0.053
0.008
0.020
0.231
-0. 158
-0. 122
-0.002
0.056
-0.075
-0. 123
-0.008
-0.015
-0.000
0. 150
-0. 104
-0.024
-0.042
0.050
XXXXXXXXXXXXXXXXXX
XXXXXXXX
XXXXX
XX
XX
XXX
XXX
XXXXXX
XXXX
XX
XX
XXXXXXXXXXX
XXXXXXX
XXXXX
XXX
XX
xx
X
XXX X
XX
XXX
X
XXXX
XXX X
XXXXX
X
XXX
XX
X
XXX
X
XX
XX
X
XX
XXXXXXX
XXX XX
XXX X
X
XX
XXX
XXX X
X
X
X
XXXXX
XXXX
XX
XX
XX
Fig(5-34) : PACF of the monthly fatalities "C4" :l,n Saudi Arabia.
225
Fig(S-3S)
st
Time series plot of the 1
difference of the monthly
fatalities "C4" in Saudi Arabia.
125+
C41
-125+
-250+
+-----------+-----------+-----------+-----------+-----------+
o
12
24
36
48
60
125+
C41
0+
-125+
-250+
+-----------+-----------+-----------+-----------+-----------+
72
84
96
108
120
60
125+
C41
0+
-125+
-250+
+-----------+-----------+
132
144
120
N* = 1
226
ACF of C41
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
+----+----+----+----+----+----+----+----+----+----+
XXXXXXXXXXX
1 .-0.404
XXX
2 -0.068
XX
0.027
3
XXX
0.076
4
XXX
5 -0.099
XX
6 -0.047
XXXX
-0. 102
7
XXX
0.069
8
XX
0.045
9
XX
10 -0.043
XXXXXXX
-0.236
11
XXXXXXXXXXXXX
0.498
12
XXX
13 -0.096
XXX X
14 -0. 101
XX
0.021
15
XXX
0.069
16
XXX
17 -0.081
XX
0.038
18
XXXXX
19 -0. 160
XX
0.034
20
XXX
0.079
21
XXXX
22 -0. 107
XXXX
-0. 125
23
XXXXXXXXXX
0.364
24
XXX
.,'"
-0.084
"o_:.::J
X
26 -0.019
X
27 -0.006
XX
0.034
28
XX
29 -0.035
X
0.014
30
XXXX
31 -0.139
XX
32 -0.027
XXX X
0.139
33
XXX
34 -0.085
XXXXXX
35 -0. 195
XXXXXXXXXXXX
0.452
36
XXXX
37 -0. 127
XX
38 -0.039
XX
39 -0.035
XXXX
0.101
40
XX
41 -0.036
X
42 -0.016
XXXX
-0.
116
43
X
0.001
44
XX
0.044
45
XX
0.025
46
XXXXXXX
47 -0.226
XXXXXXXXXX
0.356'
48
XXX
49 -0.071
XX
\
50 -0.027
Fig(5-36) : ACF of the 1st difference of the monthly fatalities "C4"
in
Saudi Arabia.
227
PACF of C41
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
:l
2
3
4
5
6
7
8
9
10
11
12
13
14
15
1,6
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
XXXXXXXXXXX
XXX XXX XX
XXXXX
X
XXX
XXX X
XXXXXXXX
-0.227
XXXXXXX
-0. 118
XXXX
-0.117
XXXX
-0.504
XXXXXXXXXXXXXX
0.031
XX
0.098
XXX
0.031
XX
0.026
XX
0.029
XX
-0. 013
X
0. 145
XXXXX
0.058
XX
0.000
X
0.042
XX
'-0.127
XXX X
-0. 162
XXX XX
0.074
. XXX
-0.032
XX
0.029
XX
0.019
X
-0.057
XX
0.006
X
-0.012
X
-0.069
XXX
-0. 140
XXXXX
-0.066
XXX
-0.036
XX
-0.224
XXXXXXX
0. 129
XXX X
0.098
XXX
0.031
XX
-0.082
XXX
0.048
XX
0.097
XXX
0.059
XX
0.056
XX
0.064
XXX
-0.077
XXX
0.074
XXX
0.024
XX
0. 056"
XX
-0.028
XX
-0.046
XX
st
Fig(5-37) : PACF of the 1
difference of the monthly fatalities "C4"
in Saudi Arabia.
-0.404
-0.277
-0. 156
0.005
-0.072
-0. 135
-0.288
228
ACF of C52
-1.0 -13.8 -13.6 -13.4 -0.2
0.13
13.2
13.4
13.6
13.8
1.13
+----+----+----+----+----+----+----+----+----+----+
1
2
3
4
5
6
7
8
9
113
11
12
13
14
15
16
17
18
19
213
21
-13.927
13.745
-0.529
13. 349
-13.233
13. 181
-13. 179
13.218
-13.2913
13.374
-13.436
13.446
-13.4131
13.327
-13.2613
13.2213
-0.202
13. 1913
-13. 176
13. 167
-0. 178
XXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXX
XXXXXXX-XXX
XXXXXXX
XXXXXX
XXXXX
XXXXXX
XXX XXX XX
XXXXXXXXXX
XXXXXXXXXXXX
XXXXXXXXXXXX
XXXXXXXXXXX
XXXXXXXXX
XXXXXXXX
XXXXXX
XXX XXX
XXXXXX
XXXXX
XXXXX
XXXXX
PACF of C52
-1.0 -0.8 -13.6 -13.4 -13.2
13.13
13.2
13.4
13.6
0.8
1.13
+----+----+----+----+----+----+----+----+----+----+
1
2
3
4
5
6
7
8
9
113
11
12
13
14
15
16
17
18
19
213
21
-13.927
-13.8138
-0.617
-0.078
0. 134
0.179
-0.256
0. 123
0.1318
-13.1385
13.1359
13.1348
-13. 1213
13.1366
13.1339
-13.1368
13.1328
13.13136
-13.1336
13.1379-13.1382
XXXXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXX
XXX
XXXX
XXXXX
XXXXXXX
XXXX
X
XXX
XX
XX
XXXX
XXX
XX
XXX
XX
X
XX
XXX
XXX
Fig(5-38) : ACF and PACF of the 12th difference of the monthly
fataJ.ities "C4 n in Saudi Arabia.
Fig(5-39)
229
SARn.1A(2,1,O)X(O,1,1)12 for the monthly fatalities "04" in
Saudi Arabia
ariMa .2,1,0 0,1,1.
12 c4 c5 c6
EstiMates at each iteration
Iteration
SSE
'ParaMeters
o
333470
0. 100
0. 100
273426
-0.050
13.029
1
223946
-13.2013
-0.044
2
185549
-13.348
-13. 124
3
164448
4
-0. 195
-13.457
5
153120
-0.545
-0.266
6
149167
-13.562
-0.296
7
148533
-0.542
-0.281
8
148452
-13.536
-0.274
9
148443
-0.535
-0.271
113
148442
-0.534
-13.2713
11
148442
-0.534
-13.270
Relative change in each estiMate less than
F ina 1 EstiMates of ParaMeters
Type
EstiMate
St. Dev.
AR
-0.5340
1
13.0867
AR
2
-0.2702
0.13869
SMA 12
0 ..8615
13.13721
0.1130
0.177
~h285
0.435
0.585
13.735
13.829
0.851
0.858
0.861
0.861
0. 861
0.131310
t-ratio
-6. 16
-3.11
11. 95
Differencing: 1 regular, 1 seasonal of order 12
No. of obs.:
Original series 144, after differencing 131
Residuals:
SS = 139789 (backforecasts excluded)
MS =
1092 OF = 128'
Modified Box-Pierce chisquare statistic
Lag
12
24
36
18.5(DF= 9)
34.4(DF=21)
46.6(DF=33)
Chisquare
48
59. 2( DF=45 )
ACF of C5 (residuals)
-1.13 -13.8 -13.6 -13.4 -13.2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
-13.1389
-0. 142
-0.2137
13.052
-0.0132
-13. 176
13.1336
0. 124
13.1331
-0.1391
-0.1347
-0.035 .
0.159
-0.085
-0.073
0.1359
0.1359
13.093
-13.053
13.007
0.015
13.0
0.2
13.4
0.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
XXX
XXXXX
XXXXXX
XX
X
XXXXX
XX
XXXX
XX
XXX
XX
XX
XXXXX
XXX
XXX
XX
XX
XXX
XX
X
X
..
230
F1g(5-39) oont.
N*
HistograM of C5
N = 131
Midpoint
-100
-80
,-60
-40
-20
0
20
40
60
80
*
****
******
**********
*************************
**********************************
*************************
*********************
****
Count
1
4
6
10
25
34
25
21
4
1
= 13
*
MTB .) nsco c5 c50
pMTB ) lot c50 c5
C50
*
2.0+
*
2~5
*36*
3255
666*
0.0+
*974
** *
-2.0+
* *
+---------+---------+---------+---------+---------+------CS
-105
N* =
-70
13
-35
0
35
70
231
:&-1g(5-40) : SARIIM(3,1 ,0)X(0 •. 1.1) 12 for the monthly fatalities "C4"
in Saudi Arabia.
EstiMates at each iteration
SSE
ParaMeters
Iteration
0. 100
0. 100
0. 100
0
334280
0.100
275243
-0.050
0.011
0.045
0. 171
1
-0.012
-0.081
0.268
2
226024
-0.200
. 186387
-0. 180
-0.074
0.404
3
-0.350
-0. 134
-0.474
-0.273
0.554
4
161100
-O,575
-0.365
-0.198
0.704
5
146189
-0.264
-0.443
0.846
6
138294
-0.639
-0.454
-0.288
-0.627
0.869
7
137754
-0.420
-0.280
-0.611
0.871
8
137575
-0.280
-0.418
0.873
137569
-0.610
9
-0.417
-0.281
0.873
-0.610
137568
10
-0.281
-0.610
-0.417
0.873
11
137568
Relative change in each estiMate less than 0.0010
Final EstiMates of ParaMeters
Type
EstiMate
St. Dev.
0. 0868
AR
-0.6100
1
AR
-0.4170
0.0964
2
-0.2807
0.0863
AR
3
SMA 12
0.8735
0.0705
t-ratio
-7.02
-4.33
-3.25
12.39
Oifferencing: 1 regular, 1 seasonal of order 12
No. of obs.:
Original series 144, after differencing 131
Residuals:
SS = 128300 (backforecasts excluded)
MS =
1010 OF = 127
Modified Box-Pierce chisquare statistic
36
12
24
Lag
11.7(OF= 8)
34.0(DF=20)
46. 1< OF=32 )
Chisquare
48
59.3(DF=44)
ACF of C5 (res1duals)
-1.0 -0.8 -0.6 -0.4 -0.2
1
2
3
4
5
6
7
8
9 ..
10
11
12
13
14
15
16
17
18
19
20
21
-0.056
-0.037
-0.089
-0. 155
-0.007
-0. 171
0.042
0.094
-0.029
-0.016
-0.040
-0.070
0. 153
-0.079
-0.039
0.094
0.030
0. 133
-0.068
0.029
-0.033
0.0
0.2
0.4
0.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
XX
XX
XXX
XXXXX
X
XXXXX
XX
XXX
XX
X
XX
XXX
XXXXX
XXX
XX
XXX
XX
XXX X
XXX
XX
XX
232
Midpoint
Count
-100
-80
-60
-40
-20
0
20
40
60
80
MTB
MTB
Fig(5-40) cont.
1
2
4
14
21
38
30
15
5
1
>
> plot
*
**
****
**************
*********************
**************************************
******************************
***************
*****
Histogram of C5
N=131
*
nscc c5 c50
c50 c5
C50
2.0+
***
*2**
3664
5394
. *4554
4272
0.0+
-2.0+
*
*
636
**
352*
*2 332
* **
2
3
--+---------+---------+---------+---------+---------+----C5
-105
MTB
-70
-35
> plot c5 c6 (C6 : The
*
35
70
predicted values. )
*
*
*
*
*
* *
2* * * *2* * *
*
* * * * 2 2 * * *2* *2 *
* **
* * 2*2 22
* ** *2 * * 2** **3 *3* *** * * * *
23
**22
*
2 * **2** * **
* **
*
* * **2
*
*
2
* *
* *
*
**
*
*
*
*
60+
C5
0+
-60+
-;
-120+
0
*
--+---------+---------+--- ------+---------+---------+----C6
60
120
180
240
300
360
Monthly fatalities in Riyadh region
Monthly injuries in Riyadh region
Monthly accidents in Riyadh region
1300
500
80
IlOO
450
70
1100
400
60
tOOD
J50
50
000
VI
~
1:
~ "u
~
300
.!
=:c
:2
·c"
.2-
800
"
.-
c
2!iO
700
40
I \
I ,
I
nllll 11 n I 11111
JO~
I I nln
I~
I~\
IIIIVIIIII"hllllllliUlllllr
200
ODD
11111
11 I III I II
11 11 'fL R U 11
11
11
I
20
150
500
. 10
100
400
JOO
ci
20
40
60
80
months
100
120
140
50+1---r--.---r--.---r--.---r&0
80
100
120
wo
40
o
20
0+1--.--.---.--r--T--'--'60
80
'00
120
140
o
20
.0
months
Fig(5-41) : Monthly acoidents, injuries, and fatalities in Riyadh region
months
N
w
w
234
ACF of C2
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
1.
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
I
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
'0.838
0.708
0.624
0.561
0.501
0.449
0. 405
0.387
0.410
0.418
' 0.428
0.423
0.381
0.371
0.385
0.346
0.334
0.320
0.307
0.268
0.262
0.211
0. 199
0.196
0. 156
0. 139
0.116
0. 087
0.054
0.056
0.040
0.035
0.024
-0.010
-0.037
-0.007
0.006
0.050
0. 069
0.065
XXXXXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXX
XXXXXXXXXXXXXX
XXXXXXXXXXXX
XXXXXXXXXXX
XXXXXXXXXXX
XXXXXXXXXXX
XXXXXXXXXXX
XXXXXXXXXXXX
XXXXXXXXXXXX
XXXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXXX
XXXXXXXXXX
XXXXXXXXX
XXXXXXXXX
XXXXXXXXX
XXXXXXXX
XXXXXXXX
XXX XXX
XXXXXX
XXXXXX
XXXXX
XXXX
XXXX
XXX
XX
XX
XX
XX
XX
X
XX
X
X
XX
XXX
XXX
Fig(5-42) : ACF ,of the monthly accidents "C2" in
Riyadh region.
235
F'ACF of C2
-1,O -O,8 -O,6 -O,4 -0,2
0,0
0,2
O,4
O,6
O,8
1,0
+----+----+----+----+----+----+----+----+----+----+
1
2
3
4
5
6
7
8
9
1O
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
3O
31
32
33
34
35
36
37
38
39
4O
O,838
O,O19
O,O87
O,045
O,OO2
O,015
O,O13
O,075
0, 156
0,O29
O,O71
O,OO0
-O, 105
O,O89
O,O89
-0,118
0, 105
-O,O2O
-O,003
-0, 101
O,059
-'O, 148
0, 102
-O,015
-0,097
O,015
-0,068
-0,O36
-0,069
0,056
-O,013
O,016
-0,053
-0,078
-O,040
0, 137
0,070
0, 123
0,O14
-0,O46
XXXXXXXXXXXXXXXXXXXXXX
X
XXX
XX
X
X
X.
XXX
XXXXX
XX
XXX
X
XXXX
XXX
XXX
XXXX
. - XXXX
XX
X
XXX X
XX
XXXXX
XXXX
X
XXX
X
XXX
XX
XXX
XX
X
X
XX
XXX
XX
XXXX
XXX
XXX X
X
XX
Fig(5-43) : PACF of the monthly accidents "C2" in Riyadh region.
"
236
Fig(5-44)
ACF and PACF of' the 1st difference of the monthly
accidents "C2'" in Riyadh region.'
ACF ofC22
-1,O -O,8 -O,6 -O,4 -O,2
0,0
0,2
O,4
0,6
0,8
1,O
+----+----+----+----+----+----+----+----+----+----+
1
2
3
4
5
6
7
8
9
1O
11
12
13
14
15
16
17
18
19
20
21
-O,138
-O, 146
-O,O48
-0.055
-0,010
-O,O37
-O,04O
-0, 124
O,O54
-O,O23
O,O22
0, 149
-o, 115
-O,O84
0,194
-O, 103
O,O1O
0, O11
O,072
-O,097
0, 132
XXXX
XXXXX
XX
XX
X
XX
XX
XXXX
XX
XX
XX
XXXXX
XXXX
XXX
XXX XXX
XXX X
X
X
XXX
XXX
XXXX
PACF of C22
-1.O -O,8 -O.6 -0.4 -O,2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
-0, 138
-O, 168
-O, 100
-O, 11O
-0,O68
-O,091
-O,097
-O,204
-0,065
-O, 134
-O,077
0, ij,12
-0, 134
-O. 157
O. 105
-0. 148
-0.026
-O.O35
0.069
-O.088
0. 128
0.0
0.2
0,4
O.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
XXXX
XXXXX
XXX
XXX X
XXX
XXX
XXX
XXXXXX
XXX
XXX X
XXX
XXX
XXXX
XXXXX
XXXX
XXXXX
XX
XX
XXX
XXX
XXXX
237
:Fig(5-45)
ARD!A(1,O,O) for the monthly accidents "02" in
Riyadh region.
ariMa 1,0,0 c2 cS c6;
EstiMates at each iteration
Iteration
SSE
ParaMeters
0
3756330
0. 1OO 660. 115
2865615
0.250 550.206
1
0.400 440.280
2
2172573
3
0.550 330.324
1677197
0.700 220.309
4
1379477
5
1280249
0.837 119.776
0.849 110.253
6
1279314
1279294
7
0.851 108.917
1279293
0.851 108.713
8
r(elative· change in each estiMate less than
Final EstiMates of ParaMeters
Type
EstiMate
St. Dev.
AR
1
0.8509
0.0446
Constant
108.713
7.878
Mean
729.32
52.85
No. of obs.:
Residuals:
144
SS =
MS =
1269061
8937
0.0010
t-ratio
19.06
13.80
(backforecasts excluded)
DF = 142
Modified Box-Pierce chisquare statistic
Lag
36
12
24.
Chisquare
8.3(DF=11)
28.3(DF=23)
41. 4( DF=35)
48
55. 6( DF=47 )
238
Fig(5-45) cont.
ACF of C5 (residuals)
-1,0 -3,8 -0,6 -0,4 -0,2
0,0
0,2
0,4
0,6
0,8
1,3
+----+----+----+----+----+----+----+----+----+----+
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
-0,060
-0,082
0,003
0,001
0,026
0,031
-0,012
-0,085
0,077
0,010
0,055
13,161
-0,079
-13,13513
13,2132
-0,067
0,036
0,039
0,094
-0,068
0, 145
-0,095
-0,002
0, 138
-0,077
0,056
0,029
0,007
-0, 101
0,073
-0.025
0,011
0,086
-0,031
-0, 181
0,050
-0,082
0,086
0,097
-0,028
-0,011
0,070
0, 108
-O,065
0,000
-0, 109
-0,039
0,097
O,018
-O,017
XXX
XXX
X
X
XX
X
X
XXX
XXX
X
XX
XXXXX
,XXX
XX
XXXXXX
XXX
XX
XX
XXX
XXX
XXXXX
XXX
X
XXXX
XXX
XX
XX
X
XXXX
XXX
XX
X
XXX
XX
XXXXXX
XX
XXX
XXX
XXX
XX
X
XXX
XXXX
XXX
X
XXX X
XX
XXX
X
X
239
His"tograM of C5
Midpoin"t Coun"t
-250
1
4
-'200
8
-150
-100
17
-50
23
34
0
50
24
100
20
150
9
200
1
250
1
300
2
MTB plo"t c5 c6
N =
Fig(5-45) cont.
144
*
****
********
*****************
***********************
**********************************
************************
********************
*********
*
*
**
( 06 : The predicted values)
)
C5
*
*
200+
*
* 2
*
* 2 **
*
* *2
2*22*2**
*****2 * **
* * *2
*
* * 2* * **2*
* 22* 22222*
2*·**2* * 2* *
* 2 3 233
* 2*
*
**
*
**
* * * *2 * ** **
*
*
* * * **2 **
*
* *
**
* **
*
*
*
*
0+
-200+
------+---------+---------+---------+---------+---------+C6
450
600
750
900
1050
1200
MTB ) plot c50 c5
C50
2.0+
24* *
342**
682
**
* *
222844
0.0+
-2.0+
3
-*
*424
* *32·
*6+3
5458
34252
*
----+---------+---------+---------+---------+---------+--C5
-200
-100
0
100
200
300
240
ACF of C3
-l.eJ -€I. 8 -€I. 6 -€I. 4 -€I. 2
. . ..,
.:..
€I. 4 eJ.6 €I. 8 1. €I
+----+----+----+----+----+----+----+----+----+----+
1
2
3
4
5
6
7
8
9
leJ
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
3eJ
31
32
33
34
35
36
37
38
39
413
€I.
€I.
€I.
€I.
€I.
712
61eJ
481
495
449
eJ.43eJ
€I. 363
€I. 348
€I. 286
eJ.311
0.270
€I. 239
€I. 198
0. 171
€I. 14eJ
€I. 142
0.096
eJ.eJ84
€I. 056
0.032
0.015
0.eJ6eJ
0.eJ33
0. 136
0.146
0. 145
0.eJ52
0.022
0. 022
0.072
0.051
eJ.eJ77
0.eJeJ9
0.eJ5eJ
0.075
13. 134
0.1eJ9
0.eJ88
eJ.eJ68
. €I. 146
Fig(5-46)
eJ.eJ
~
XXXXXXXXXXXXXXXXXXX
XXXXXXXXXXXXXXXX
XXXXXXXXXXXXX
XXXXXXXXXXXXX
XXXXXXXXXXXX
XXXXXXXXXXXX
XXXXXXXXXX
XXXXXXXXXX
XXXXXXXX
XXXXXXXXX
XXXXXXXX
XXXXXXX
XXXXXX
XXXXX
XXXX
XXXXX
XXX
XXX
XX
XX
X
XXX
XX
XXXX·
XXXXX
XXXXX·
XX
XX
XX
XXX
XX
XXX
X
XX
XXX
XXX X
XXXX
XXX
XXX
XXXXX
ACF of the monthly ilijur1.es ·"CJ": in Riyedh region.
241
F'ACF of C3
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
0.712
0.209
-0.025
0.218
0.038
0.033
-0. 023
0.041
-0.057
0. 102
-0.023
-0.056
0.010
-0.035
-0.028
0.034
-0.061
-0.010
0.008
-0.060
-0.003
0. 134
-0.070
0.245
0.068
-0.097
-0.119
-0.056
-0.001
0.076
-0.012
0.024
-0.069
0.055
0.057
0.086
-0.033
-0.046
0.041
0. 121
XXXXXXXXXXXXXXXXXXX
XXXXXX
XX
XXXXXX
XX
XX
XX
XX
XX
XXXX
XX
XX
X
XX
XX
XX
XXX
X
X
XX
X
XXXX
XXX
- XXXXXXX
XXX
XXX
XXXX
XX
X
XXX
X
XX
XXX
XX
XX
XXX
XX
XX
XX
XXXX
Fig(5-47) : PACF of the monthJ.y injuries "C:}" in Riyadh region.
Fig(5-48)
242
Time series plot of the 1st difference of the monthly injurues
"e)" inRiyadh region.
C31
100+
0+
-100+
+---------+---------+---------+---------+---------+---------+
10
20
30
40
50
60
o
C31
100+
0+
-100+
+---------+---------+---------+---------+---------+---------+
60
70
80
90
C31
100+
0+
-100+
+-----:..---+---"------+---------+
120
H*
=1
130
140
150
100
110
120
243
.
st
Fi G(5-49) : ACF and PACF of the 1
difference of the monthly
injuries nC3" in Riyadh region.
ACF of C31
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
1.
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
XXXXXXXXX
XXX
XXXXXXXX
XXX
XXX
XXX X
XXXX
XXX
XXXX
XXX
XX
XX
X
XX
XX
XXX
XX
XX
X
XXX
XXX
-0.321
0.069
-0.264
0.061
-0.066
0.113
-0.101
0.099
-0. 125
0.094
-0.034
0.027
-0.015
0.021
-0.032
0.085
-0.025
0.021
-0.007
-0.067
-0.094
F'ACF of C31
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
+-~
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
-0.321
-0.038
-0.283
-0. 135
-0. 127
-0.027
-0. 121
-0.006
-0. 105
-0.025
-0.003
·-0.041
0.002
0.002
-0.011
0.075
0.062
0.045
0.086
-0.022
-0. 132
XXXXXXXXX
XX
XXXXXXXX
XXXX
XXXX
XX
XXXX
X
XXXX
XX
X
XX
X
X
X
XXX
XXX
XX
XXX
XX
XXXX
0.2
0.4
0.6
0.8
1.0
244
Fig(5-50)
ARIMA(.3,1, 1)' for the monthly injuries "0)" in
Ri:vadh region.
ariMa 3, 1, 1 c3 c5 c6;
EstiMates at each iteration
ParaMeters
Iteration
SSE
0.100
0. 100
0.
100
0
410696
0.076
0.061
1
389758
-0.050
0.056
0.046
380825
-0.200
2
375763
-0.350
0.037
0.039
3
372294
-0.500
0.018
0.035
4
369531
-0.650
-0.002
0.033
5
367170
-0.800
-0.023
0.033
6
365240
-0.950
-0.044
0.035
7
-0.050
347146
-0.883
-0. 154
8
-0. 115
337016
-0.785
-0.195
9
-0. 159
331327
-0.666 . -0.192
10
-0.535
-0. 169
-0. 186
327113
11
-0.138
323072
-0.401
:-0.206
12
-0. 104
-0.222
13
318935
-0.269
-0.235
-0. 138
-0.068
14
314661
310305
-0.011
-0.030
-0.248
15
0.008
-0.258
16
306122
0.111
0.049
-0.263
17
303137
0.226
-0.258
18
302924
0.251
0.062
- 0. 065
-0.256
19
302914
0.257
-13.256
302914
0.258
0.066
20
302914
0.258
0.066
-0.255
21
0.066
-El. 255
22
302914
0.258
Relat.ive change in each est.iMat.e less t.han 0.0010
Final Est.iMates o'f ParaMeters
Type
EstiMat.e
St. Oev.
AR
1
0.2585
0. 1371
0.0987
AR
2
0.0660
-0.2554
0.0938
AR
3
0:7001
0. 1247
MA
1
0. 100
-0.005
-0. 134
-0.272
-0.413
-0.556
-13.699
-0.845
-0.695
-0.545
-0.395
-0.245
-0.095
0.055
0.205
0.355
0.505
0.655
0.690
0.698
0.700
0.700
0.700
t-rat.io
1. 89
0.67
-2.72
5.61
Oifferencing: 1 regular difference
No. of obs.:
Original series 144, after differencing 143
Residuals:
SS = 300938 (backforecasts excluded)
MS =
2165 OF = 139
Modified Box-Pierce chisquare statistic
12
24
Lag
36
2.7(OF= 8)
18.3(OF=20)
42.0(OF=32)
Chisquare
48
52. 6( OF=44 )
245
Fig(5-50) cont.
ACF of C5
(res1duals)
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
0.002
-0.014
-0.006
0.007
-0.026
-0.007
-0.087
0.030
-0.073
0.053
-0.002
-0.001
0.021
0.007
-0.001
0.074
-13.1333
-0.023
-0.010
-0. 171
-0.078
X
X
X
X
XX
X
XXX
XX
XXX
XX
X
X
XX
X
X
XXX
XX
XX
X
XXXXX
XXX
N = 143
Hist.ograM of C5
Midpoint.
-100
-80
-60
-40
":'-20
Count.
2
o
12
14
14
31
20
27
40
60·
80
100
120
140
15
12
160
6
4
4
0
1
1
**
******
************
**************
**************
*******************************
***************************
***************
************
****
****
*
*
246
Fig(5-50) cont.
MTB
)
plot c5 c6
The predicted values.)
( c6
200+
C5
*
*
100+
*
*
*
*
*
*
0+
*
*
*
* *
*
**
*
*
*
**
*
* *
*
* * * 2* * *
** **2 * * * * **
* ** 42 *3*3
**
* *
*2 * '"'
*22* 23252** *
* *3*2** * *
*
* ***32 **
*
*
* * * 2*2 2
*
* * *
~
*
*
*
**
*
-100+
*
*
------+---------+---------+---------+---------+---------+C6
120
180
240
300
360
420
MTB ) nsco c5 c50
MTB ) plot c50 c5
C50
2.0+
363
**
**2 **
*
*
*
5443
4584
598*
0.0+
*3538*
2824
462
2
-2.0+
***
*
*
-+~
-100
N* = 1
* 2*
-50
0
50
100
150
-CS
247
ACF of C3
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
33.
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
0.520
0.374
0. 164
0. 195
0.158
0.162
0. 104
0. 134
0.082
0. 170
0. 154
0. 159
0. 131
0. 121
0. 127
0. 162
0. 116
0.090
0.000
-0.062
-0.055
0.065
0.008
0. 171
0. 174
19.235
0.058
0. 002
-0.067
-0.040
-0.035
0.002
-0. 128
-0.049
-0.056
0.039
0.008
0. 018
0.053
0. 157
0.089
0. 137
0.092
0.078
-0.038
-0.019
0.014
0.085
0.064
0. 125
Fig(5-51 )
XXXXXXXXXXXXXX
XXXXXXXXXX
XXXXX
XXX XXX
XXXXX
XXXXX
XXX X
XXXX
XXX
XXXXX
XXXXX
XXXXX
XXXX
XXXX
XXXX
XXXXX
XXXX
XXX
X
XXX
XX
XXX
X
XXXXX
XXXXX
XXXXXXX
XX
X
XXX
XX
XX
X
XXXX
XX
XX
XX
X
X
XX
XXXXX
XXX
XXX X
XXX
XXX
XX
X
X
XXX
XXX
XXXX
ACF of the monthly injuries "C3,,"in Riyadh region
after removing the first 17 observations.
I
248
F'ACF of C3
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
XXXXXXXXXXXXXX
XXXXX
0. 143
XXXX
-0. 107
XXXXX
0. 146
XX
0.041
XX
0.023
X
-0.011
XXX
0.076
XX
-0.029
XXXX
0. 128
XX
0.038
X
0.000
XX
0.038
X
0.007
XX
0.041
XXX
0.066
XX
-0.031
XX
-0.027
XXX
-0.074
XXXX
-0.110
X
0.002
XXXXX
0. 148
XXXX
-0. 123
XXXXXXX
0.237
XXX
0.099
X
0.014
XXXXX
-0. 169
XXX
-0.072
XXX
-0.062
XX
-0.031
XX
0.057
X
-0.015
XXX
XX
-0. 152
XXX
0.085
X
0.014
XX
0.042
X
-0.019
X
0.013
XXXX
0.104
XXXX
0. 121
XXXX
-0. 126
XXX
0.091
XXX
0.072
XX
-0.022
X
-0.013
XX
0.024
X
0.. 006
X
-0.002
XX
0.030
XX
-0.026
Fig(5-52) : PACF of the monthly injuries na)" in Riyadh region
after removing the first 17 observations.
0.520
249
~RIl,A(1.0)
Fig(5-53)
for the monthly injuries "e3" in J.iyadh region
after removing the first 17 observations.
MTB ) ariMa 1,0,0 c3 c5 c6;
EstiMates 'at each iteration
SSE
ParaMeters
I terat ion
329761
0,100 287.041
o
0.250 239,150
292078
1
270733 '
0,400 191.258
2
3
265432
0.515
154.554
4
265419
0.521
152.700
5
265419
0,521
152.608
Relative change in each estiMate less than
Final EstiMates of ParaMeters
St, Oev,
Type
EstiMate
0,5210
Af<
1
0,O765
152, 608
4,089
Constant
Mean
318,570
8,536
No, of obs,:
Residuals:
0,0010
t-ratio
6,81
37,32
127
SS =
MS =
265419
2123
Cbackforecasts excluded)
OF = 125
Modified Box-Pierce chisquare statistic
Lag
36
12
24
56, 7C OF=35 )
Chisquare
15, 1C OF=l1 )
31. 8C OF=23)
48
71. 6C OF=47 )
ACF of C5 (residuals).
-1,0 -O,8 -0.6 -O,4 -0,2
O,0
O,2
+-~
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
-0.075
0. 169
-0, 125
0.109
0,018
0,098
-0,038
0,099
-0,073
0, 131
0.032
0,076
0,027
0,024
0.014
0,109
0,021
0,068
-0.018
-0,069
-0,097
XXX
XXXXX
XXXX
XXXX
X
XXX
XX
XXX
XXX
XXXX
XX
XXX
XX
XX
X
XXXX
XX
XXX
X
XXX
XXX
O,4
0,6
0,8
1,0
250
Fig(5-53) cont.
HistograM of C5
N = 127
Midpoint
-100
-80
-60
-40
-20
0
Count
3
4
20
18
8
40
60
80
100
120
140
160
MTB
MTB
11
12
19
·35
7
6
1
2
0
1
}
nsco c5 c50
}
plot c50c5.
***
****
***********
************
*******************
***********************************
******************
********
*******
******
***
*
C50
*
*
*
*
2**
1. 6+
*
423*
*552
663
3+
2364
246*
*342
0.0+
-1.6+
*
*
* **
*25
22
----+---------+---------+---------+---------+---------+--c!
-100
-50
0
50
100
150
251
ACF of C4
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
1
2
3
4
5
6
7
8
9
10
11
0.055
12
29
0.070
0.076
-O,022
-0.092
-0.068
-0.086
-0.063
-0. 123
-0.073
0.028
0.073
0. 079
0.067
0.,;)91
0.064
0.020
0.037
-0.040
30
-0.052
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
XXXXXXXXXXXXX
XXXXXXXXX
XXXXXXXX
XXXXXX
XXXXX
XX
XXX
XXX X
XX
XX
XX
XXX
XXX
XX
XXX
XXX
XXX
XXX
XXXX
XXX
XX
XXX
XXX
XXX
XXX
XXX
XX
XX
XX
XX
0.474
0.312
0.271
0.193
0.160
0.034
0.093
0. 108
0.043
0.054
Fig(5-54)
I
ACF of the monthly fatalities "C4" in Riyadh region.
252
F'ACF of C4
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
0.474
0.113
0. 113
0.011
0.033
-0. 115
0. 101
0.041
-0.036
0.019
0.020
0.019
0.036
-0. 101
-0. 121
0.007
-0.027
0.028
-0.082
0.026
0.095
0.115
0.020
-0.001
0.013
-0;015
0.002
0.034
-0. 128
-0.044
XXXXXXXXXXXXX
XXXX
XXXX
X
XX
XXXX
XXXX
XX
XX
X
X
X
XX
XXXX
XXXX
X
XX
XX
XXX
XX
XXX
XXX X
X
X
X
X
X
XX
XXXX
XX
Fig(5-55) : PACF of the monthly fatalities "C4" in Riyadh region.
Pig(5-56)
253
at
Time series plot of the 1
difference of the monthly
fatalities "C4" in Riyadh region.
25.0+
r.
C41
0.0+
-25.0+
-50.0+
+-----------+-----------+-----------+-----------+-----------+
o
12
24
36
48
60
25.0+
C41
~l.
0+
-25.0+
-50.0+
+-----------+-----------+-----------+-----------+-----------+
60
72
84
96
108
120
25.0+
C41
0.0+
-25.0+
"
-50.0+
+-----------+-----------+
120
132
144
254
ACF of C41
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
1.0
+-~
-0.358
-0. 119
0.053
-0.042
0.076
-0. 168
0.044
0.069
-0.077
0.015
-0.014
11
0.013
12
0.090
13
14 -0.026
j~ .;;)
-0.077
0.033
16
17 -0.012
0.064
18
19 -0.096
20 -0.055
0.036
21
0.064
22
0.010
23
-0.051
24
0.060
25
0.002
26
27 -0.043
0.087
28
-0.055
29
30 -0.028
1
2
3
4
5
6
7
8
9
10
XXXXXXXXXX
XXX X
XX
XX
XXX
XXXXX
XX
XXX
XXX
X
X
X
XXX
XX
XXX
XX
X
XXX
XXX
XX
XX
XXX
X
XX
XX
X
XX
XXX
XX
XX
Fig(5-57) : ACF of the 1st difference of the monthly fatal.ities "C4"
in Riyadh region.
255
PACF of C41
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
-0.358
-0.283
-0. 128
-0. 129
0.008
-0. 189
-0. 117
-0.044
-0.096
-0.084
-0.088
-0.090
0.038
0.053
-0.065
-0.040
-0.057
0.041
-0.051
-0.132
-0. 162
-0.032
0.007
-0.036
-0.005
-0.036
-0.051
0. 110
0.038
-0.043
XXXXXXXXXX
XXXXXXXX
XXXX
XXX X
X
XXXXXX
XXXX
XX
XXX
XXX
XXX
XXX
XX
XX
XXX
XX
XX
. XX
XX
XXX X
XXXXX
XX
X
XX
X
XX
XX
XXXX
XX
XX
st
flg(5-58) : PACF of the 1
difference of the monthly fatalities "C4"
in·· Riyadh region.
256
Fig(5-59)
ARTh!A(O,1,2) for the monthly fatalities "C4" in
Riyadh region.
arl.Ma 0, 1.,2 <:4 c5 c6;
Est.iMat.es at. each it.erat.ion
It.erat.ion
SSE
ParaMet.ers
,
0
14427.5
0. 100
0. 1OO
O,250
1
13070.2
0. 169
0.400·
2
12190.7
0.205
11799.3
0.545
3
0.200
11773.4
4
0.568
0.206
5
0.572
0.216
11766.
6
11763.2
0.574
0.222
7
11762. 1
0.576
0.225
8
11761. 7
0.577
0.228
11761. 5
9
0.577
0.229
11761. 4
0.577
1O
0.230
11
11761. 4
0.578
0.231
11761. 4
0.578
12
0.231
13
11761. 4
0. 578
0.231
Relat.ive change in each est.iMat.e less t.han
°
Final Est.iMat.es of ParaMet.ers
Type
Est.iMat.e
St.. Dev.
MA
1
0.5779
0.0820
MA
2
0.2311
0.0822
11).0010
t.-rat.io
7.05
2.81
Oifferencing: 1 regular difference
No. of obs.
Original series 144, aft.er differencing 143
Residuals:
SS = 11737.7 (backforecast.s excluded)
MS =
83.2 OF = 141
Modified Box-Pierce chisquare st.at.ist.ic
Lag
12
24
36
Chisquare
7.4(OF=10)
16.9(DF=22)
26. 5( DF=34 )
48
39. 9( DF=46 )
257
Fig(5-59) cont.
ACF of C5 (residuals)
-1.0 -0.8 -0.6 -0.4 -0.2
0.0
0.2
0.4
0.6
0.8
1.0
+----+----+----+----+----+----+----+----+----+----+
:[
2
3
4
5
6
7
8
9
1O
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
X
XXX
XXX
XX
X
XXXXX
XX
0.003
0.063
0.066
-0.029
0.015
-0. 171
-0.020
0.001
-0.091
-0.021
-0.023
0.012
0.053
-0.047
-0. 103
-0.036
-0.067
-0.023
-0. 131
-0.077
0.023
0.084
0.064
0.021
0.093
0.045
0.004
0.073
-0.043
-0.041
X
XXX
XX
XX
X
XX
XX
XXXX
XX
XXX
XX
XXXX
XXX
XX
XXX
XXX
XX
XXX
XX
X
XXX
XX
XX
HistograM of C5
Midpoint
-20
-15
-10
-5
°
5
10
15
20
25
30
35
N
Count
1
5 .
19
34
22
32
17
8
3
o1
1
=
143
N*
=1
*
*****
*******************
**********************************
**********************
********************************
*****************
********
***
*
*
258,
Fig(S-59) cont.
MTB
>
MT8 }
nseD cS c50
c50 c5
plo~
C50
*2 *
2.0+
*
394
2+63
0,0+
34673
4+6
2554
3*62
*5
***
-2.0+
*
*
+---------+---------+---------+---------+---------+------C5
-24
-12
0
12
24
36
N* = 1
MT8
}
plot cS
c6
( c6
The predicted values.)
1.10+
*
C5
·20+
0+
-20+
:..
*
** *
*
**
* *
* **
*
* *
*
* *2
* *
2
** * *32 *
2*
* 2***2 3 3*422* * * **
*
* *
* ** 2*2**2** * ** 2
* * *3*33*3** * *2* *
* * 3***2* ***
* **** **2 *
*
**
*
*
*
+---------+---------+---------+---------+---------+------C6
24.0
32.0
40.0
48.0
8.0
16.0
259
Fig(5-60):ACF and PACF of the first difference of the daily fatalities
of Riyadh area.
+-.~
..
"',
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260
Fig.(5-61): ARlMA(O,1,1) for the first difference of "C4" the daily
fatalities in Riyadh area
at each
E5~imates
11.:;>2('3. i;
itel~0.on
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262
CHAPTER VI
CONCLUSIONS AND RECOMMENDATIONS
This final chapter gives the main results and findings of
this study.
In general,
the application of linear
regression
analysis and a time series representation using ARIMA modelling
are
the
main
two
statistical
methods
we
have
used
to
find
appropriate models for the various sets of data.
For
the
investigation
using
regression
analysis
considered 7 predictor variables and 3 response variables.
R2 _ criterion ...as the basis of obtaining optimum models.
we
The
By
using Aitkin's adequate subset approach, we found that for most of
these models the final representations were in terms of two or
R2 values expressed in
three predictor variables and that the
percentage terms lay between 58% - 98%.
The number of registered
driving
licences
variables
in
the
issued
X3
models
which
vehicles
are
the
fit
X2 and
most
the
the
number
frequent
number
of
of
predictor
accidents,
injuries and fatalities in the different regions of Saudi Arabia,
wherein for most of the regions X2 and X3 have a positive effect
in the regression mode Is.
The
Durbin-Watson
test
for
serial
correlation
residuals was applied to all the models selected by
technique.
correlation.
of
the
the above
It revealed l i tUe evidence of the presence of such
263
For
the
elimination
backward
and
forward
selection
procedures we find that the predictor variable Xl, the population
size,
contributes
most
injuries and fatalities
in
fitting
of all
the
the
number
regression
of
accidents,
models
in Saudi
Arabia, as well as in the Riyadh and Makkah regions,
except for
the
the
models
which
fit
the
number
of
fa tali ties
in
l~akh
region.
We found that X5, the number of the transport vehicles, is
the most contributive predictor variable with a positive effect in
the
models
which
fit
the
number
of
accidents,
injuries
and
fatalities in the Makkah region.
The population size, the number of registered vehicles and
the number of issued driving licences are ell increasing with time
at a very high rate.
Unless
some
proper
planning and strict
measure to control these variables are introduced, their effect on
the
numbers
of
aCCidents,
injuries
and
fatalities
will
also
increase.
A Poisson regression using an iteratively weighted
squares
technique was
used
accidents in Saudi Arabia.
were the population size,
to
fit
the numbe,r of
modelling
is
not
traffic
The predictor variables in this case
the number of registered vehicles and
the number of issued driving licences.
Poisson
road
least
sui table
to
It was
fit
the
found
that
number of
the
road
accidents in Saudi Arabia as indicated by the log-likelihood ratio
statistic.
The dummy variables technique was used to see if there are
any
differences
in
the
number
of
accidents,
fatali ties in the different regions of Saudi Arabia.
injuries
and
It is found
that there are differences between the different regions, but the
264
indicated
presence
of
interaction
between
the
dummy
variables
(representing the regions) and the other predictor variables prevent these differences being represented in a very simple form.
For
the
time
series
analysis
using
ARIMA
modelling
procedures we obtain representations for the same three response
variables,
namely numbers of accidents,
injuries and
fatalities
using selected sets of data which are appropriate for the purpose
of time series analysis.
model
diagnostics
Model identification, model fitting and
are
appropriate model for
the
three
stages
in
time series analysis.
determining
The
an
final models
arrived at for each of the three regions used in the study are set
out in Tables (5-3) to (5-5) on page 177.
The data representation of Chapter III gives an indication
of the severi ty of the accidents, which lead to extensive human
losses in injuries and fatalities.
be updated.
The values given there can now
In Saudi Arabia during the 17 years from 1971-1987
there were 209,653 injuries and 37,608 fa tali ties resulting from
252,058 road traffic accidents.
In general terms, we note that· the number of road traffic
accidents, injuries and fa tali ties in Saudi Arabia increased by
factors of 8, 5 and 5 respectively from 1971 to 1987.
In
the
15
year
period
studied,
the
data
for
accident,
injury and fatality rates were first expressed in terms of unit
population for each region, and then it was found that a logarithmic
ttansformation was
appropriate
prior to
carrying
out
an
analysis of variance.
For
the
transformed
data,
highly
significant
emerged both between regions and between years.
difference
It is worthy
265
of note that the region means are in the same rank order for
accident rate and injury rate, except for the interchange of the
Makkah
and Riyadh
regions
(these
having
the
highest
values).
Oddly, Riyadh drops down to second smallest for fatality rate, the
rankings of the remaining regions otherwise being as for accident
rate.
We
conclude
that
cannot be attributed
the
differences
to anyone
among
region,
but
the
six
regions
that each region
contributes to this difference as indicated by Duncan' s Multiple
Range Test.
For the above three rates we find that no difference exists
between the Qaseem and North regions.
The difference between the years can be attributed mainly to
the year 1971 for the accident and injury rates, where it stands
out as different from the remaining 14 years.
In
addition,
we
can
conclude
that
there
are
no
major
differences among the years of the following periods: (1975-1982)
for the accident rate, (1972-1977) and (1978-1985) for the injury
rate and (1978-1985) for the fatality rate.
steadily increasing trend
There is, however, a
throughout the whole of the 15 year
period.
Combining the
findings
of
our
literature
own
study
recommendations which it
is
review in Chapter 11 with
we
hoped
can
summarize
will
the
eventually
the
following
reduce
the
severity of road traffic accidents in Saudi Arabia, and possibly
also in other developing countries.
266
The accident reporting system is deficient.
documentation of traffic accidents is necessary.
Better
2 -
Since a large percentage of drivers do not hold driving
licences, strict law enforcement is essential for
reduction of accidents.
3 -
Speed limits in the centre of cities and on highways
should be monitored.
4 -
Safety education is necessary for drivers, users and
pedestrians to ensure a safer traffic environment.
5 -
Traffic enforcement must take place in the cities and
on the highways.
This study can be considered as a first step for further
studies
to
predict
(and
modify)
the
injuries and fatalities in Saudi Arabia.
position
of
accidents,-
267
APPENDIX A :Population of Saudi Arabia
We are
overall and
study (i.e.
helpful in
problems.
interested in finding the population of Saudi Arabia
the population of it' s regions in the period of the
1971-1985).
The figures of this population will be
analysing the road traffic accidents and related
To do this, we use the multipurpose census of 1974, the
yearly growth rates, and the model (1).
To estimate the
population of the regions of .Saudi Arabia and the country overall
we use the well-known model, Nutfaji (1981).
(1)
Pn
where,
Pn: estimated population of the calender year n. (n=1971, ... ,1985)
Pn:, population of the base year no' (no = 1971)
ri: yearly growth rate, where i=l, 2, 3, and
rl = 0.029 for the period (1971-1975)
r2 = 0.030 for the period (1976-1980)
r3 = =.032 for the period (1981-1985)
U.N. Demographic yearbook (1974).
Using a simple Fortran Programme, we can find the estimated
population of each region in the period of (1971-1985) and the
overall population of Saudi Arabia. The population are given in
Table (A - 1)
(1)
AI-Rawaithy, M.A.(1979) population of Saudi Arabia;
Geographic and Demographic Study, Dar Allewaa,
Riyadh.
(2)
Nutfaji, M.A. (1981) Projection of Saudi Population
by Sex and Age (1975-2000), Research Center, King
Saud University, Riyadh.
268
TABLE (A -1 )
Year
Riyadh
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1167708
1201572
1236418
1272275
1309171
1349754
1390247
1431954
1474913
1519159
1586124
1636881
1689259
1743316
1799101
Makkah
Dammam
North
Qaseem
South
1609940
1656629
1704672
1754108
1804977
1860931
1916758
1974261
2033488
2094492
2186818
2256797
2329012
2403540
2480453
764213
786376
809181
832648
856795
883355
909855
937151
965265
994223
1038049
1071266
1105546
1140923
1177432
957919
985699
1014285
1043700
1073967
1107260
1140477
1174692
1209932
1246229
1301164
1342801
1385769
1430114
1475877
529181
544528
560319
576569
593289
611681
630031
648932
668400
688452
718799
741801
765537
790035
815316
1340318
1379188
1419185
1460342
1502692
1549275
1595753
1643625
1692933
1743721
1820585
1878844
1938965
2001012
2065044
Saudi
Arabia
6436283
6622937
6815004
7012642
7216010
7439703
7662894
7892780
8129560
8373444
8742549
9022312
9311016
9608970
9916454
269
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