Analysis on road accident data by severity of injuries 2010 Wayamba University of Sri Lanka

1. Road Accident data by severity of injuries
2010
STAT 3232
Data Analysis and Preparation of Statistical
Report
Wayamba University of Sri Lanka
Group B:
142069
142129
142140
142153
142187

2. 1. Introduction
2. Aim
3. Objectives
4. Project design/ Data Collection
5. Project Function
6. Data Collection
7. Analysis
8. Conclusion
CONTENT2

3. Introduction
 Road accidents can be happened due to various reasons. The
purpose of this presentation is to learn about how vary the road
accident data by severity of injuries in 2010, due to some factors
such as Grievous injuries and non Grievous injuries. The Death
male was measured in 25 districts.
 We content this report under five chapters namely introduction,
Aim, Objectives, Project design, Project Function, Data Collection,
analysis and conclusion.
 Analyze the data by using multiple regressions.
3

4. Aim
 Find the equation of the Death males in all
districts considering the grievous and non
grievous injuries.
4

5. Objectives
 Identify the factors which affect to death male
 Find an equation for the dependent variable.
 Fit the adequate model and reduce the death
male.
5

6. Project design/Data Collection
 Dependent variable
 No of Death Male
 Independent variables
 No of Grievous injury male
 No of Non grievous injury male
 Secondary data was used
6

7. Project Function
 DeathMale=β0+β1*(Grievous_Male)+β2*(Non
_Grievous_Male)
 β0 is a constant
 β1 is a coefficient of Grievous injury male
 β2 is a coefficient of Non Grievous injury male
7

8. Analysis
 Fundamental Analysis
 Advanced Analysis
8

9. Fundamental Analysis
 Relationship between selected dependent variable and
independent variables
9

10.  Grievous injury male and Non Grievous injury male seems to have
positive linear relationship with Death male.
 We can conclude that there is a positive relationship between Death male
and Grievous injury male.
 We can conclude that there is a positive relationship between Death male
& Non Grievous injury.
Deaths_Male Grievous_Injury_Male Non_Grievous_Injury_Male
Deaths_Male
Grievous_Injury_Male
Non_Grievous_Injury_Male
1.0000000
0.9213329
0.9475252
0.9213329
1.0000000
0.9624212
0.9475252
0.9624212
1.0000000
10

11. Advanced Analysis
Checking Suitable Model
 Forward Selection
Start: AIC=218.15
Deaths_Male ~ 1
Table 1: Deaths_Male~1
Degree of
Freedom
Sum of Sq RSS AIC
+ Non_Grievous_Injury_Male 1 127652 14530 163.13
+ Grievous_Injury_Male 1 120692 21490 172.91
<none> 142182 218.15
11

12. Step: AIC=163.13
Deaths_Male ~ Non_Grievous_Injury_Male
Table 2:Deaths_Male~Non_Grievous_Injury_Male
Call:
lm(formula = Deaths_Male ~ Non_Grievous_Injury_Male, data = road2)
Coefficients:
(Intercept) Non_Grievous_Injury_Male
9.8347 0.1374
Degree of
Freedom
Sum of Sq RSS AIC
<none> 14530 163.13
+ Grievous_Injury_Male 1 170.89 143690 164.83
12

13.  Backward Selection
Start: AIC=164.83
 Deaths_Male ~ Grievous_Injury_Male +Non_Grievous_Injury_Male
Table 3: Deaths_Male~Grievous_Injury_Male+Non_Grievous_Injury_Male
Degree of
Freedom
Sum of Sq RSS AIC
- Grievous_Injury_Male 1 170.9 14530 163.13
<none> 14360 164.83
-Non_Grievous_Injury_Male 1 7130.7 21490 172.91
13

14. Step: AIC=163.13
Deaths_Male ~ Non_Grievous_Injury_Male
Table 4:Deaths_Male~Non_Grievous_Male
Call:
lm(formula = Deaths_Male ~ Non_Grievous_Injury_Male, data = road2)
Coefficients:
(Intercept) Non_Grievous_Injury_Male
9.8347 0.1374
Degree of
Freedom
Sum of Sq RSS AIC
<none> 14530 163.13
-Non_Grievous_Injury_Male 1 127652 142182 218.15
14

15.  Both Algorithms
Start: AIC=218.15
Deaths_Male ~ 1
Table 5: Deaths_Male~1
Df Sum of Sq RSS AIC
+
Non_Grievous_Injury_Male
1 127652 14530 163.13
+ Grievous_Injury_Male 1 120692 21490 172.91
<none> 142182 218.15
15

16. Step: AIC=163.13
Deaths_Male ~ Non_Grievous_Injury_Male
Table 6: Deaths_Male~Non_Grievous_Male
Coefficients:
(Intercept) Non_Grievous_Injury_Male
9.8347 0.1374
Df Sum of Sq RSS AIC
<none> 14530 163.13
+ Grievous_Injury_Male 1 171 14360 164.83
- Non_Grievous_Injury_Male 1 127652 142182 218.15
16

17. Model Identification
 Deaths_Male = 9.834723 +
0.137354*(Non_Grievous_Injury_Male)
Coefficients:
Table 7: Coefficients of parameters
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 25.13 on 23 degrees of freedom
Multiple R-squared: 0.8978, Adjusted R-squared: 0.8934
F-statistic: 202.1 on 1 and 23 DF, p-value: 7.019e-13
Estimate Std. Error t value Pr(>|t|)
(Intercept) 9.834723 7.554829 1.302 0.206
Non_Grievous_Injury_
Male
0.137354 0.009663 14.215 7.02e-13
17

18. CHECKING THE SIGNIFICANCE OF
THE MODEL
H0: Coefficient of non grievous injury male = 0 Vs
H1: Coefficient of non grievous injury male ≠ 0
Since p-value = 7.02e-13<0.05 we can reject H0. So we can conclude
that the Coefficient of non grievous injury male is not equal zero at 5%
level of significance.
18

19. CHECKING THE SIGNIFICANCE
OF EACH COEFFICIENT
Testing Hypothesis
H0: Constant = 0 Vs
H1: Constant ≠ 0
Since p-value = 0.206>0.05, we do not have enough evidence to reject
H0. So we concluding that constant is zero at 5% level of significance.
Testing Hypothesis for coefficient value of independent
variables
H0: Coefficient is not significant Vs
H1: Coefficient is significant
 Since p-value = 7.02e-13<0.05, we have enough evidence to reject
H0. So we concluding that coefficient is significance at 5% level.
19

20. Best Model
 Deaths Male =
0.137354*(Non_Grievous_Injury_Male)
Checking Coefficient of determination
 Multiple R-squared: 0.8978
 89.78% of variation for death injury male is explained by
the model
20

21. CHECKING ASSUMPTIONS
 NORMALITY OF RESIDUALS
21

22. INDEPENDENCE AND CONSTANT VARIANCE OF
RESIDUALS (Randomness of residuals)
22

23. MULTICOLINEARITY
 There is a high correlation between independent variables.
 Multicollinearity exists.
Deaths_Male Grievous_Injury_Male Non_Grievous_Injury_Male
Deaths_Male
Grievous_Injury_Male
Non_Grievous_Injury_Male
1.0000000
0.9213329
0.9475252
0.9213329
1.0000000
0.9624212
0.9475252
0.9624212
1.0000000
23

24. Conclusion
 Grievous injuries factor does not affect to the
death male according to the advanced
analysis.
 Non grievous factor is affect to the death male
among deaths cause by road accidents.
24