2 14 85 35
1 13 75 56
2 7 95 48
4 5 100 29
2 7 70 43
0 18 75 57
3 6 110 37
2 14 100 40
4 4 100 25
1 14 80 30
1 19 70 34
3 10 95 32
2 10 85 36
4 3 70 27
1 15 90 45
2 14 75 60
3 5 100 29
4 9 85 41
1 3 75 26
0 16 70 58
2 9 75 46
1 5 70 53
0 14 70 48
0 8 60 52
2 4 75 36
0 7 65 50
3 6 90 34
5 3 120 35
2 1 85 41
3 6 70 29
3 6 85 34
0 13 70 53
2 5 75 34
4 2 95 35
4 1 100 53
2 2 85 36
1 5 70 34
1 5 75 27
0 6 70 56
1 3 80 44
0 8 70 53
0 11 75 37
3 1 95 38
2 3 90 43
2 3 85 25
1 6 80 36
0 5 75 54
0 14 70 45
0 10 70 38
1 9 75 57
Number of Accidents vrs Vehicle Maintenance
It is observed that there is a negative linear relationship between the number of accidents and the age of driver.
Number Accidents vrs Average speed of driver
It is observed that there is a positive linear relationship between the number of accidents and the average speed of driver.
Number Accidents vrs Age of Driver
It is observed that there is a negative linear relationship between the number of accidents and the age of driver.
Regression
Correlations
DESCRIPTION OF MODEL
The regression model is of the form
Y = B0 + B1 X1 + B2 X2 + B3 X3
with Y being the number of accidents encountered by the drivers and the dependent variable. X1,X2,X3 represents the number of times they maintained their vehicles, the average speed at which they drove their vehicles and their ages respectively;they represent the independent variables.
Y= -1.745-0.0651X1+0.06454X2-0.0311X3 R2 = 0.695
(1.51) (0.028) (0.010) (0.013) S.e
The estimated regression model above depicts the relationship between the predictor variables and the response variable and their standard errors.
The value of R (0.812) depicts a strong linear relationship between all the predictor variables and the response variable.
An R2 value of 0.659 means that the regression model fits well to the set of data points and that 65.9 percent of the variation of the number of accidents the drivers had is explained by the multiple regression model. The Adjusted R2 means that 63 percent of the regression model can be predicted with the estimated regression model when the number of variables is taken into account.
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TESTS OF SIGNIFICANCE
The test of the overall significance and viability of the estimated model is as follows;
H0 : Bj = 0
H1 :Bj 0
for at least one,j = 1,2,3
From the anova table,the p-value is given to be 0.00,since it is less than= 0.05,we reject the null hypothesis and conclude that the number of accidents a driver encountered is at least dependent on one of the following; the number of times they maintained their vehicles, the average speed at which they drove their vehicles and their ages.
To find out the strength of each predictor variable with the response variable,t-tests are carried out as follows;
H0 : Bk = 0
H1 :Bk 0
To test whether vehicle maintenance is related to the number of accidents encountered by the drivers,take k = 1.
H0 : B1 = 0
H1 :B1 0
Since a p-value of 0.023 is less than 0.05,we reject H0 and conclude that the number of accidents encountered by the drivers depends on the number of times they maintained their vehicles.
To test whether the average speed of drivers is related to the number of accidents encountered by the drivers,take k = 2.
H0 : B2 = 0
H1 :B2 0
Since a p-value of 0.00 is less than 0.05, we reject H0 and conclude that the number of accidents encountered by the drivers depends on the average speed they drove their vehicles.
To test whether age of driver is related to the number of accidents encountered by the drivers,take k = 3.
H0 : B3 = 0
H1 :B3 0
Since a p-value of 0.023 is less than 0.05,we reject H0 and conclude that there is evidence from the data that the number of accidents encountered by the drivers depend on the age of the driver.
CORRELATION ANALYSIS
The correlations table depicts the strength of the relationship that exist between the number of accidents encountered by the commercial vehicles as the dependent variable,and the number of times they maintained their vehicles, the average speed at which they drove their vehicles and their ages.
It is easily observed that the number of times the drivers maintained their
vehicles is negatively related to the number of times they had accidents but the Pearson Correlation Coefficient of 0.489 in absolute value shows that the relationship is a weak one.This suggests that drivers who maintained their cars more often experienced less number of accidents.
It is also observed that the average speed at which the commercial drivers drove on the Accra Kumasi Highway is positively related to the number of accidents they encountered.Thus,the faster they drove,the more they risked getting an accident.The Pearson Correlation Coefficient of 0.739 reveals that the relationship between the average speed at which the commercial drivers drove and the number of accidents they encountered is very strong.
The age of the drivers is observed to be negatively related to the number of times they had accidents and the Pearson Correlation Coefficient of 0.513 in absolute value shows that this relationship is a good one.
Nevertheless, the correlation between each variable and itself is a perfect one with a Correlation Coefficient of 1.
PREDICTION
To predict the number of accidents a driver of 25 years of age who maintained his vehicle 4 times and drove at an average speed of 100 km/h the data is put into the regression model as follows;
Y= -1.745-0.0651X1+0.06454X2-0.0311X3
Y = -1.745-0.06514(4)+0.06454(100)-0.0311(25)
=3.67
Hence a driver of 25 years of age who maintained his vehicle 4 times and drove at an average speed of 100 km/h may encounter 3.67 accidents which is 0.33 away from the observed value of 4.Hence,with a residual error of just 0.33,the regression model can be said to be adequate with vehicle maintenance and average speed of driver being most influencial in the model.
RESIDUAL PLOTS
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CONCLUSION
The number of accidents encountered by vehicles on the Accra Kumasi highway are related to number of times the drivers maintained their vehicles, the average speed at which they drove their vehicles and their ages.
From the model it is observed that the more a driver did vehicle maintenance,the less he got accidents.Younger drivers got more.The faster a driver drove,the more he encountered accidents.
ROAD SAFETY PROPOSALS
In order to minimize road accidents;
- Drivers who ply the highway must be forced to maintain their vehicles more often by way of conduction of regular checkups at the exit points of the lorry station,so that vehicles that are not in good condition are stopped from embarking on the journey.
- There should be more speed limit indications and road safety signs at various points on the highway.An uncompromising law enforcement agency should be posted at various segments of the highway to make sure defaulters are made to face the law.
- Young drivers must be educated on the dangers they impose on themselves whenever they drive at high speeds.
REFERENCES
Econometric Models and Forecasts (Irwin & Mc-Graw-Hill); Robert S. Pindyck & Danile.
Elementary Statistics (Mc Graw-Hill); Allan G. Bluman
