Nizan Zioni: Question 5

To what extent do the road lighting conditions, the time of week (mid-week/weekend), weather conditions, and the volume of vehicles on the road (the explanatory variables) influence the severity of the accident (the dependent variable)?

For this question, We’ve used 2 datasets from the UK, between the years 2005-2010

Descriptive Statistics:

## .
## Darkness Lighting: Unknown        Darkness Lights Lit 
##                         19                       3063 
##      Darkness Lights unlit       Darkness No Lighting 
##                         30                          7 
##                   Daylight 
##                       6881

	Freq	% Valid	% Valid Cum.	% Total	% Total Cum.
1	8811	88.11	88.11	88.11	88.11
2	1001	10.01	98.12	10.01	98.12
3	54	0.54	98.66	0.54	98.66
4	18	0.18	98.84	0.18	98.84
5	8	0.08	98.92	0.08	98.92
6	1	0.01	98.93	0.01	98.93
7	16	0.16	99.09	0.16	99.09
8	65	0.65	99.74	0.65	99.74
9	26	0.26	100.00	0.26	100.00
	0	NA	NA	0.00	100.00
Total	10000	100.00	100.00	100.00	100.00

	Number_of_Vehicles
Mean	1.803300e+00
Std.Dev	6.858981e-01
Min	1.000000e+00
Q1	1.000000e+00
Median	2.000000e+00
Q3	2.000000e+00
Max	8.000000e+00
MAD	0.000000e+00
IQR	1.000000e+00
CV	3.803572e-01
Skewness	1.733886e+00
SE.Skewness	2.449120e-02
Kurtosis	1.097654e+01
N.Valid	1.000000e+04
Pct.Valid	1.000000e+02

	Freq	% Valid	% Valid Cum.	% Total	% Total Cum.
Darkness Lighting: Unknown	19	0.19	0.19	0.19	0.19
Darkness Lights Lit	3063	30.63	30.82	30.63	30.82
Darkness Lights unlit	30	0.30	31.12	0.30	31.12
Darkness No Lighting	7	0.07	31.19	0.07	31.19
Daylight	6881	68.81	100.00	68.81	100.00
	0	NA	NA	0.00	100.00
Total	10000	100.00	100.00	100.00	100.00

	Freq	% Valid	% Valid Cum.	% Total	% Total Cum.
1	1065	10.65	10.65	10.65	10.65
2	1421	14.21	24.86	14.21	24.86
3	1510	15.10	39.96	15.10	39.96
4	1599	15.99	55.95	15.99	55.95
5	1514	15.14	71.09	15.14	71.09
6	1553	15.53	86.62	15.53	86.62
7	1338	13.38	100.00	13.38	100.00
	0	NA	NA	0.00	100.00
Total	10000	100.00	100.00	100.00	100.00

	Freq	% Valid	% Valid Cum.	% Total	% Total Cum.
1	3076	30.76	30.76	30.76	30.76
2	6081	60.81	91.57	60.81	91.57
3	675	6.75	98.32	6.75	98.32
4	117	1.17	99.49	1.17	99.49
5	32	0.32	99.81	0.32	99.81
6	5	0.05	99.86	0.05	99.86
8	14	0.14	100.00	0.14	100.00
	0	NA	NA	0.00	100.00
Total	10000	100.00	100.00	100.00	100.00

Inferential Statistics

## [1] "Chi Square and kramer's correlation:"

## 
##  Pearson's Chi-squared test
## 
## data:  data_inference$weather and data_inference$accident_severity
## X-squared = 3.7588, df = 2, p-value = 0.1527

## Warning in chisq.test(data_inference$number_of_vhcls,
## data_inference$accident_severity): Chi-squared approximation may be incorrect

## 
##  Pearson's Chi-squared test
## 
## data:  data_inference$number_of_vhcls and data_inference$accident_severity
## X-squared = 107.32, df = 6, p-value < 2.2e-16

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  data_inference$weekend and data_inference$accident_severity
## X-squared = 0.85156, df = 1, p-value = 0.3561

Conclusions:

For Light conditions and accident severity indication: association is significant. For weather conditions and accident severity indication: association is not significant. For Number of Vehicles and accident severity indication: association is significant. For Weekend / weekday indication and accident severity indication: association is non-significant.

Logistic Regression

## 
## Call:
## glm(formula = accident_severity ~ weather + weekend + number_of_vhcls, 
##     family = "binomial", data = data_inference)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -0.6089  -0.5403  -0.4701  -0.4550   2.9735  
## 
## Coefficients:
##                               Estimate Std. Error z value Pr(>|z|)    
## (Intercept)                   -1.48496    0.09867 -15.050  < 2e-16 ***
## weatherOther                   0.04935    0.23027   0.214   0.8303    
## weatherRain without high wind  0.19045    0.10039   1.897   0.0578 .  
## weekendweekend                 0.06890    0.06485   1.062   0.2881    
## number_of_vhcls               -0.36548    0.05248  -6.964 3.32e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 7005.2  on 9999  degrees of freedom
## Residual deviance: 6948.5  on 9995  degrees of freedom
## AIC: 6958.5
## 
## Number of Fisher Scoring iterations: 5

	x
(Intercept)	0.227
weatherOther	1.051
weatherRain without high wind	1.210
weekendweekend	1.071
number_of_vhcls	0.694

x
0.1597645
0.1358222
0.0983310
0.1441138
0.1358222
0.1165558

Discussion and conclusion from the logistic regression results:

According to the logistic regression results, it can be concluded that the variables: light = daylight and number of vehicles, are significant. On top of that, based upon the odds-ratio measure, we found that day-light reduced the probability to a severe accident to 78.2% of an accident not in daylight. Also we’ve found that the more vehicles involved in a car accident, the less chance for a severe car accident. specifically - the every can involved in a car accident, the chance for a severe car accident reduces to 69.5%.

As for the confusion matrix, according to the prediction procedure, none of the observations, yielded into an event (in other words - for all observations severe accident = 0). To handle this, we’ve chosen to split the predicted results by the 90th percentile, which indicates 90% chance for a non-sever accident. the relevant value is 0.15155 which is 15.155%. In other words - 90% of the observations generate a prediction probability of no more than 15.155%.

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction    0    1
##          0 8603 1063
##          1  279   55
##                                          
##                Accuracy : 0.8658         
##                  95% CI : (0.859, 0.8724)
##     No Information Rate : 0.8882         
##     P-Value [Acc > NIR] : 1              
##                                          
##                   Kappa : 0.0256         
##                                          
##  Mcnemar's Test P-Value : <2e-16         
##                                          
##             Sensitivity : 0.96859        
##             Specificity : 0.04919        
##          Pos Pred Value : 0.89003        
##          Neg Pred Value : 0.16467        
##              Prevalence : 0.88820        
##          Detection Rate : 0.86030        
##    Detection Prevalence : 0.96660        
##       Balanced Accuracy : 0.50889        
##                                          
##        'Positive' Class : 0              
##

Project

Nizan