## 4 Analysis and Results
### Prediction Models  
Binary logistic regression and CART models were used for predicting the chances of young victims, ranging from 15 to 44 years of age, being involved in RTCs. For the development of the models, crash types and reasons with less than 5% occurrence in the dataset were merged into a single category of \"others\". As stated above, 5% is the commonly applied significance criteria for statistical analysis. The parameters taken for modeling and their description/coding are provided in Table 4. The coding for crash reasons and types was kept the same as that of the original dataset for backtracking purposes. The composition of model development-validation samples was 75-25%. It was found that approximately 74% of the samples included victims between the ages of 15 and 44 years. Hence, we ensured that samples that were selected for development and validation were of the same proportion for the accurate representation of actual data. The number of samples was selected randomly within each category of RTCs. Figure 6: Age-wise distribution of RTC victims. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & \
\begin{tabular}{c} **Number of Major** \\ **Injuries** \\ \end{tabular} &
\begin{tabular}{c} **Number of Deaths** \\ **Number of Deaths** \\ \end{tabular} \\ \hline Total & 22,787 & 3579 \\ \hline Number of RTCs & 3245 & 756 \\ \hline Average per RTC * & 7 & 4 \\ \hline Range & 0–46 & 0–13 \\ \hline Severity Index = deaths/no. of RTCs & 0.89 & \\ \hline Number of fatal and major injury & 1333 & \\ RTCs per year & 352 & \\ \hline Number of deaths per year & 1193 & \\ \hline Number of deaths per 100,000 people & 311 & \\ \hline \hline \end{tabular}  
* Number of major injuries/number of RTCs with major injuries; same was used for the average deaths per RTC.  
\end{table} 
Table 3: Descriptive statistics for RTCs, major injuries, and deaths. Equation (5) shows the utility equation for the logistic regression model. The number of deaths was not found to have a significant effect on the model at a 5% significance level. Equation (5) is:  
\[ \begin{split}\text{U}=-1.03+0.08\ (\text{fatal})-1.64\ (\text{collision})+0.01\ (\text{vehicle overturn})+0.60\ (\text{hit pedestrians})\\ -0.08\ (\text{other types})-0.002\ (\text{hit road fence})-0.30\ (\text{not leaving sufficient gap})\\ -0.18\ (\text{sudden turning})+0.04\ (\text{speeding})+0.25\ (\text{not giving way})+0.14\ (\text{other reasons})\\ +0.04\ (\text{number of injuries})\end{split}  \tag{5}\]  
The \(t\)-statistics and corresponding \(p\)-values for the coefficients of the utility equation are given in Table 5. It can be observed that some of the reasons and types of traffic crashes did not have a statistically significant coefficient in the model, for example, vehicle overturn, hit road fence, and any other types of traffic crashes; however, they were kept in the equation because they were fed to the model under the categorical variables of reasons and types. This strategy was chosen to reduce the number of variables used for the model. Consequently, it was not possible to exclude specific categories of the same variable. However, after the first trial, as shown in Equation (5), we decided to include a separate binary variable for each reason and type of crash and recalibrate the utility equation by omitting the reasons and types that did not have a significant effect on the previous utility equation. The utility equation, acquired in this manner, is shown as Equation (6) as follows:  
\[ \begin{split}\text{U}=1.07+0.84\ (\text{hit pedestrians})-0.40\ (\text{not leaving sufficient gap})-0.23\ (\text{sudden turning})\\ +0.04\ (\text{number of injuries})+0.09\ (\text{fatal})\end{split}  \tag{6}\]