Multivariate regression techniques for analyzing auto crash variables in nigeria

Journal of Natural Sciences Research www.iiste.org
ISSN 2224-3186 (Paper) ISSN 2225-0921 (Online)
Vol.1, No.1, 2011

Multivariate Regression Techniques for Analyzing Auto-
Crash Variables in Nigeria
Olushina Olawale Awe1* Mumini Idowu Adarabioyo2

1. Department of Mathematics, Obafemi Awolowo University Ile-Ife, Nigeria.

2. Department of Mathematical Sciences, Afe Babalola University, Ado Ekiti,
Nigeria.
*E-mail of the corresponding author: olawaleawe@yahoo.co.uk

Abstract
It is unequivocally indisputable that motor vehicle accidents have increasingly become a
major cause of concern for highway safety engineers and transportation agencies in
Nigeria over the last few decades. This great concern has led to so many research
activities, in which multivariate statistical analysis is inevitable. In this paper, we explore
some regression models to capture the interconnectedness among accident related
variables in Nigeria. We find that all the five variables considered are highly interrelated
over the past decade, resulting in a high risk of mortality due to auto-crash rate. The
result of our analysis, using an appropriate statistical software, also reveals that the
simple regression models capture the relationships among the variables more than the
multiple regression model considered.

Key Words: Multivariate Model, Analyzing, Regression, Data, Accident, Rate.

1. Introduction

Multivariate techniques and statistical tests are needed to analyze data in many areas of human
endeavor in order to provide descriptive and inferential procedures which we can use to detect
behavioral patterns or test hypotheses about parameters of interest. Controversy has continued to trail
the exact number of deaths recorded yearly through road accident in Nigeria with World Health
Organization(WHO), the National Union of Road Transport Workers(NURTW) and the Federal road
Safety Commission of Nigeria(FRSCN) giving conflicting reports. While the international agency claimed
that 32,000 died yearly through road accidents in Nigeria, the FRSCN insisted that the country had only
recorded between 4000 and 5000 deaths from road accidents in the last three years. The president of
the National Union of Road Transport Workers of Nigeria(NURTW) once claimed that, “despite the fact

19 | P a g e
www.iiste.org

Vol.1, No.1, 2011
that not all deaths and accidents on our roads are officially reported, 8, 672 people were said to have
lost their lives to road accidents in Nigeria in 2003, while another 28,215 people sustained different
degrees of injuries within the period. The number of people dying as a result of road accident in
Nigeria has reached an alarming proportion as accident rates increases towards the end of the
year especially as from the month of September (Ojo, 2008). Analysis of the traffic crashes
recorded over a five year period of 2000- 2006 showed that 98,494 cases of traffic crashes were
recorded out of which 28,366 were fatal and resulted into deaths(FRSCN Report,2009).This
revealing statistics shows that Nigeria is placed among the fore front nations experiencing the
highest rate of road tragedies in the world. This paper focuses on determining the degree of
association between those who are killed in road crashes and variables like the number of
vehicles involved, number of accidents recorded, number injured and the particular month the
accident occurred. The rest of the paper is organized as follows: section two considers the data
and methodology used in the study, section three enumerates the main results, section four is on
the discussion and findings from the study, while section five concludes the study. The various
analysis performed are presented and labeled as exhibits below the conclusion.

2. Data and Methodology

2.1 Data

Accidents Statistics covering s period of five years were collected (2003-2007) from
Lagos State Command of the Federal Road Safety Corps. The data were then summed up
according to the particular month the accident occurred, thereby giving us a sample size
of twelve. The essence of this is to determine the effect of a particular month in the year
on accident situation in Lagos State as the month increases to December.

2.2 Methodology

A simple linear regression equation of the dependent variable on each of the other factors
and a multiple regression equation was fitted on all the independent variables. The simple
linear regression is a special case of the multiple linear regression(Rencher,2002),so we
consider first simple linear regressions of the dependent variable on each of the
independent variables.The dependent variable for the analysis is the number of people

20 | P a g e
www.iiste.org

Vol.1, No.1, 2011
killed and the independent variables are x1 , x2 , x3 and x4 (what each variable represents
is given below).

Y = f(X1+ X2+ X3+ X4)----------------------------(1)

The hypothesis tested in the study is that: there is no significant relationship between
Number of people killed and the variables x1 , x2 , x3 and x4 which could not be
explained on the basis of chance alone.

The Multiple linear regressions is defined by:

Y =α + X β + X β
i i i i 2 2
+ X β
3 3
+ X β +ε
4 4 i
-------------------(2)

Where Y i _ killed
= the number people killed in the accident

X 1i _ accident
= the number of accidents

X 2 injured
_ = the number of injured persons

X 3i _ vehicle
=Number of vehicles involved

X 4i _ month
= the particular month the accident occurred.

ἑi is the random error term of the model

After identifying the hypothesis for testing, statistical analysis was performed on all the
variables (Y, X1, X2, X3 and X4). The results of the analyses are presented in exhibits 1,
2, 3, 4 and 5.

The simple linear regression is carried out between Y i _ killed
and each of the independent

variables X 1i _ accident
, X 2i _ injured , X 3i _ vehicle and X 4i _ month

and the results are displayed in Tables 1, 2, 3 and 4.
21 | P a g e
www.iiste.org

Vol.1, No.1, 2011
2.3 Classical Assumptions of the Linear Regression Model

The assumptions of the linear regression model are stated as follows:

• The model has a linear functional form.
• The independent variables are fixed.
• Independent observations.
• Normality of the residuals.
• Homogeneity of residuals variance.
• No Multicollinearity.
• No autocorrelation of the errors.
• No outlier distortion.

3. Main Results

This section discusses the results of the various regression models fitted to the accident
data.

3.1 Linear regression of Y i _ killed
on X 1i _ accident
.

In the analysis the coefficient of correlation(r) between the two variables is 0.326 and the
coefficient of determination (r2) is 0.1063. r2 is small that is the amount of variation in the
number killed accounted for by the number of accident is 10.63% with probability value
of 0.151 greater than alpha (0.05) so the association is not so statistically significant.

The regression equation is

Y i _ killed
=1786.116 + 0.559 X 1i _ accident ------------------------------(3)

that is for every unit change in the number of accident, there is a positive 0.559 change in
the number of those killed. This is a direct relationship. The model is not significant at
P(0.05) as the P-value is 0.301 greater than alpha. See exhibit 1.

22 | P a g e
www.iiste.org

Vol.1, No.1, 2011
3.2 Linear regression of Y i _ killed on X 2 i _ injured
.

In the analysis, the coefficient of correlation(r) between the two variables is 0.702 and the
coefficient of determination (r2) is 0.493. r2 is large that is the amount of variation in the
number killed accounted for by the number injured is 49.3% with probability value of
0.011 less than alpha (0.05) so the association is statistically significant.

The regression equation is Y i _ killed
=1005.283 +1.674 X 2i _ injured --------------(4)

that is for every unit change in the number injured; there is a positive 1.674 change in the
number of those killed. This is a direct relationship. The model is significant at P(0.05) as
the P-value is 0.011less than alpha. See Exhibit 2.

3.3. Linear regression of Y i _ killed
on X 3i _ vehicle
.

number killed accounted for by the number of vehicle involved is 44.3% with probability
value of 0.011 less than alpha (0.05) so the association is statistically significant.


Y i _ killed
=845.674 +0.688 X 3i _ vehicle
--------------------------(5)

that is for every unit change in the number of vehicle, there is a positive 0.688 change in
the number of those killed. This is a direct relationship. The model is significant at
P(0.05) as the P-value is 0.011 less than alpha. See exhibit 3.

3.4 Linear regression of Y i _ killed
on X 4i _ month
.


23 | P a g e
www.iiste.org

Vol.1, No.1, 2011
number killed accounted for by the particular month is 45.5% with probability value of
0.016 less than alpha (0.05) so the association is statistically significant.


Y i _ killed
= 2445.132 +69.318 X 3i _ vehicle -----------------------------(6)

that is for every unit change in the number of vehicle, there is a positive 69.318 change in
the number of those killed. This is a direct relationship. The model is significant at
P(0.05) as the P-value is 0.016 less than alpha. See exhibit 4.

3.5 Multiple Linear Regression Analysis of Y i _ killed
on all the explanatory variables.

In the analysis, the coefficient of correlation(r) between the two variables is 0.0.79 and
the coefficient of determination (r2) is 0.591. r2 is large, that is the amount of variation in
the number killed accounted for by all the independent variables is 59.1% with
probability value of 0.135 greater than alpha (0.05) so the association is not statistically
significant.

The multiple regression equation is

Y i _ killed
=739.489 +0.075 X 1i _ accident +0.657 X 2i _ injured

+0.39 X 3i _ vehicle +15.576 X 4i _ month (6)

There is positive correlation between Y i _ killed
and all other independent variables. The P-

value of all variables except X 1i _ accident
are less than alpha and so shows statistically

significant relationship. The p-value of X 1i _ accident
is 0.151 greater than alpha and shows

that there is no statistically significant relationship between the number of people who
were killed and the number of vehicles involved.

4. Discussion of Findings

24 | P a g e
www.iiste.org

Vol.1, No.1, 2011
Our findings reveal that the Multiple Linear Regression Model fitted is not statistically
significant. However, the relationship between each variable and the Y i _ killed
separately

are statistically significant in except for the variable X 1i _ accident . The variance accounted

for by the variable Y i _ killed
was low in all the variables. The correlation matrix (Exhibit

5) more accurately justifies the hypothesis of positive correlation between all the
independent variables and the dependent variable. The correlation of those who were
killed with the injured, the number of vehicles and the month the accidents occurred were
strongly positive (Exhibits 2, 3 and 4). The implications of these findings is that the more
vehicles involved in an accident the more people are killed and as the months approaches
December the more people are killed in road accident in Nigeria. The overall probability
value of the model is 0.135 which is greater than the alpha value of 0.05, so the model is
not relevant. However, there may be many more variables affecting number of people
killed in an accident Y i _ killed
that needs to be explored in further studies.

5.0 Conclusion.

From our analysis, we have seen that the overall model (Multiple Linear Regression
Model) fitted for the accident data is not significant, though there is positive and strong
correlation between the dependent variable and each of the independent variables. This
suggests that there are other variables that actually account for deaths resulting from
auto-crash in Lagos State, Nigeria, which if included in the model will make it more
relevant. These variables need to be explored to form a more robust model for predicting
factors affecting number of people killed as a result of auto-crash in Lagos State, Nigeria.

References

Anyata, B. U.et al (1986); A Case for Increased Investment on Road Usage Education
in

Nigeria, Proceedings of the First International Conference Held in University of

Benin, Nigeria.

25 | P a g e
www.iiste.org

Vol.1, No.1, 2011
Alvin.C. Rencher (2002):Methods of Multivariate Analysis.2nd Edition.Bringham
Young University. A John Wiley Publications.

Brussels, (2006); Commission of the European Communities Proposal for a Directive
of the

European Parliament and of the Council on Road Infrastructures Safety. Management.
[SEC(2006) 1231/1232]

Hohnsheid, K. J, (2003): Road Saftey Impact Assessment. Bergisch Gladbach,
Bundesanstalt

Strassenwesen. (Internet report)

Reurings M, (2006): Modelling the Number of Road Accidents using Generalized
Linear

Models. SWOV, Leidschendan

Rob E. (2005): Accident Prediction Models and Road Safety Assessment (Internet
Report)

Slefan. C. (2006): Predictive Model of Injury Accidents on Austrian Motorways.
KFV. Vienna.

Vikas Singh, (2006); Statistical Analysis of the Variables Affecting Infant Mortality
Rate in

United States. Journal of the Department of Health Services Administration,
University of Arkansas Medical Services

Wichert S, (226): Accident Prediction Models For Portuguese Motorways. LNEC,
Lisbon

www.makeroadsafe.org

26 | P a g e
www.iiste.org

Vol.1, No.1, 2011
Exhibit 1

Model Summaryb

Change Statistics
Adjusted Std. Error of R Square
Model R R Square R Square the Estimate Change F Change df1 df2 Sig. F Change
1 .326a .106 .017 367.27931 .106 1.187 1 10 .301
a. Predictors: (Constant), X1_ACCDT
b. Dependent Variable: Y_KILLED

Coefficientsa

Unstandardized Standardized
Coefficients Coefficients Correlations Collinearity Statistics
Model B Std. Error Beta t Sig. Zero-order Partial Part Tolerance VIF
1 (Constant) 1786.116 1023.944 1.744 .112
X1_ACCDT .559 .513 .326 1.090 .301 .326 .326 .326 1.000 1.000
a. Dependent Variable: Y_KILLED

ANOVAb

Sum of
Model Squares df Mean Square F Sig.
1 Regression 160133.4 1 160133.360 1.187 .301a
Residual 1348941 10 134894.089
Total 1509074 11
a. Predictors: (Constant), X1_ACCDT

27 | P a g e
www.iiste.org

Vol.1, No.1, 2011
Residuals Statisticsa

Minimum Maximum Mean Std. Deviation N
Predicted Value 2664.2156 3065.2813 2895.7500 120.65479 12
Std. Predicted Value -1.919 1.405 .000 1.000 12
Standard Error of
106.032 237.487 143.759 44.506 12
Predicted Value
Adjusted Predicted Value 2177.2100 3041.1980 2870.2766 226.39478 12
Residual -564.965 677.78455 .00000 350.18708 12
Std. Residual -1.538 1.845 .000 .953 12
Stud. Residual -1.869 2.419 .029 1.143 12
Deleted Residual -834.152 1164.790 25.47340 509.89718 12
Stud. Deleted Residual -2.198 3.564 .089 1.438 12
Mahal. Distance .000 3.682 .917 1.210 12
Cook's Distance .000 2.103 .286 .618 12
Centered Leverage Value .000 .335 .083 .110 12

EXHIBIT 2

Model Summaryb

Change Statistics
1 .702a .493 .443 276.47418 .493 9.742 1 10 .011
a. Predictors: (Constant), X2_INJURED

28 | P a g e
www.iiste.org

Vol.1, No.1, 2011
Coefficientsa

1 (Constant) 1005.283 610.904 1.646 .131
X2_INJURED 1.674 .536 .702 3.121 .011 .702 .702 .702 1.000 1.000

ANOVAb

Sum of
1 Regression 744694.5 1 744694.535 9.742 .011a
Residual 764379.7 10 76437.971
Total 1509074 11
a. Predictors: (Constant), X2_INJURED


Predicted Value 2403.0457 3288.5745 2895.7500 260.19128 12
Standard Error of
79.831 176.882 109.159 29.982 12
Predicted Value
Residual -420.170 396.56958 .00000 263.60779 12
Std. Residual -1.520 1.434 .000 .953 12
Stud. Residual -1.587 1.499 -.017 1.039 12
Deleted Residual -458.388 432.93729 -11.49076 316.14455 12
Stud. Deleted Residual -1.741 1.615 -.029 1.086 12
Mahal. Distance .000 3.586 .917 1.074 12
Cook's Distance .001 .551 .105 .153 12

29 | P a g e
www.iiste.org

Vol.1, No.1, 2011

EXHIBIT 3

Model Summaryb

Change Statistics
1 .703a .494 .443 276.32907 .494 9.763 1 10 .011
a. Predictors: (Constant), X3_VEHICLE

Coefficientsa

1 (Constant) 845.674 660.937 1.280 .230
X3_VEHICLE .688 .220 .703 3.125 .011 .703 .703 .703 1.000 1.000

ANOVAb

Sum of
1 Regression 745496.7 1 745496.714 9.763 .011a
Residual 763577.5 10 76357.754
Total 1509074 11
a. Predictors: (Constant), X3_VEHICLE


Predicted Value 2314.8884 3233.5776 2895.7500 260.33138 12
Standard Error of
79.858 202.291 107.818 34.666 12
Predicted Value
Residual -763.578 220.83029 .00000 263.46943 12
Std. Residual -2.763 .799 .000 .953 12
Stud. Residual -3.162 .897 -.036 1.096 12
Deleted Residual -1000.00 278.41348 -23.73454 350.88265 12
Stud. Deleted Residual -.951 .888 .239 .498 11
Mahal. Distance .002 4.978 .917 1.389 12
Cook's Distance .000 1.548 .192 .452 12

30 | P a g e
www.iiste.org

Vol.1, No.1, 2011

EXHIBIT 4

Model Summaryb

Change Statistics
1 .675a .455 .401 286.69806 .455 8.360 1 10 .016
a. Predictors: (Constant), X4_MONTH

Coefficientsa

1 (Constant) 2445.182 176.450 13.858 .000
X4_MONTH 69.318 23.975 .675 2.891 .016 .675 .675 .675 1.000 1.000


Predicted Value 2514.5000 3277.0000 2895.7500 249.93026 12
Standard Error of
83.626 155.683 114.262 26.497 12
Predicted Value
Residual -391.091 378.18182 .00000 273.35587 12
Std. Residual -1.364 1.319 .000 .953 12
Stud. Residual -1.576 1.498 .000 1.050 12
Deleted Residual -538.200 487.93985 -.34125 333.19846 12
Stud. Deleted Residual -1.725 1.614 -.015 1.100 12
Mahal. Distance .019 2.327 .917 .847 12
Cook's Distance .002 .520 .114 .156 12

31 | P a g e
www.iiste.org

Vol.1, No.1, 2011
ANOVAb

Sum of
1 Regression 687116.5 1 687116.477 8.360 .016a
Residual 821957.8 10 82195.777
Total 1509074 11
a. Predictors: (Constant), X4_MONTH

EXHIBIT 5

Model Summaryb

Change Statistics
1 .769a .591 .357 297.07324 .591 2.525 4 7 .135
a. Predictors: (Constant), X4_MONTH, X1_ACCDT, X3_VEHICLE, X2_INJURED

Coefficientsa

1 (Constant) 739.489 1850.432 .400 .701
X1_ACCDT .075 .478 .044 .158 .879 .326 .059 .038 .752 1.330
X2_INJURED .657 2.108 .276 .312 .764 .702 .117 .075 .075 13.384
X3_VEHICLE .390 .367 .399 1.064 .323 .703 .373 .257 .417 2.401
X4_MONTH 15.576 84.752 .152 .184 .859 .675 .069 .044 .086 11.639

32 | P a g e
www.iiste.org

Vol.1, No.1, 2011
ANOVAb

Sum of
1 Regression 891306.7 4 222826.671 2.525 .135a
Residual 617767.6 7 88252.509
Total 1509074 11
a. Predictors: (Constant), X4_MONTH, X1_ACCDT, X3_VEHICLE, X2_INJURED

Correlations

Y_KILLED X1_ACCDT X2_INJURED X3_VEHICLE X4_MONTH
Pearson Correlation Y_KILLED 1.000 .326 .702 .703 .675
X1_ACCDT .326 1.000 .220 .472 .218
X2_INJURED .702 .220 1.000 .683 .955
X3_VEHICLE .703 .472 .683 1.000 .627
X4_MONTH .675 .218 .955 .627 1.000
Sig. (1-tailed) Y_KILLED . .151 .005 .005 .008
X1_ACCDT .151 . .246 .061 .248
X2_INJURED .005 .246 . .007 .000
X3_VEHICLE .005 .061 .007 . .014
X4_MONTH .008 .248 .000 .014 .
N Y_KILLED 12 12 12 12 12
X1_ACCDT 12 12 12 12 12
X2_INJURED 12 12 12 12 12
X3_VEHICLE 12 12 12 12 12
X4_MONTH 12 12 12 12 12

33 | P a g e
www.iiste.org

Multivariate regression techniques for analyzing auto crash variables in nigeria

More Related Content

Viewers also liked (14)

Similar to Multivariate regression techniques for analyzing auto crash variables in nigeria (20)

More from Alexander Decker (20)

Recently uploaded (20)

Multivariate regression techniques for analyzing auto crash variables in nigeria