# Improving the Resilience of High-Speed Rail Systems from a Configuration Perspective
## 4 Results  
### Multiple Regression Analysis  
This study correlated the perceptions of driving variables with resilience improvement. Table 4 shows that all Pearson correlations between driving variables and resilience improvement are positive and significant at a level of 1%. The highest correlation is between FR and resilience improvement (0.795) and the lowest is between TS and resilience improvement (0.564).  
Under the premise of ten driving variables correlated with resilience improvement, multiple regression analysis was carried out to test the relative importance of the driving variables to resilience improvement. As shown in Table 5, the adjusted R\({}^{2}\) is statistically significant at a level of 1%, meaning the model fits well. The variance inflation factor (VIF) value of OS is bigger than five, indicating that problems from multicollinearity may occur in estimating the beta coefficients [73]. Nevertheless, the rest of variables received a VIF value less than five, meaning that they cannot cause multicollinearity issues. To test the relative contribution of each driving variable, standardized slope coefficients were analyzed. Three driving variables are statically significant at a confidence level of 1%, i.e., PA, FR, and AT. Most variables were not significant in the multiple regression analysis, indicating that the relationships between most of driving variables and resilience improvement may be nonlinear. Hence, solely focusing on one single variable and discussing its relative importance is meaningless.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline  & TS & QC & EM & OS & OE & SO & DW & PA & FR & AT & RI \\ \hline TS & 1.000 & & & & & & & & & & \\ QC & 0.636 ** & 1.000 & & & & & & & & & \\ EM & 0.616 ** & 0.809 ** & 1.000 & & & & & & & & \\ OS & 0.533 ** & 0.737 ** & 0.784 ** & 1.000 & & & & & & & \\ OE & 0.487 ** & 0.611 ** & 0.622 ** & 0.714 ** & 1.000 & & & & & & \\ SO & 0.434 ** & 0.613 ** & 0.630 ** & 0.682 ** & 0.544 ** & 1.000 & & & & & \\ DW & 0.518 ** & 0.771 ** & 0.733 ** & 0.773 ** & 0.618 ** & 0.697 ** & 1.000 & & & & \\ PA & 0.555 ** & 0.763 ** & 0.773 ** & 0.767 ** & 0.688 ** & 0.674 ** & 0.790 ** & 1.000 & & & \\ FR & 0.524 ** & 0.750 ** & 0.746 ** & 0.814 ** & 0.711 ** & 0.657 ** & 0.791 ** & 0.818 ** & 1.000 & & & \\ AT & 0.554 ** & 0.715 ** & 0.720 ** & 0.730 ** & 0.653 ** & 0.613 ** & 0.713 ** & 0.753 ** & 0.750 ** & 1.000 & & \\ RI & 0.564 ** & 0.754 ** & 0.707 ** & 0.731 ** & 0.643 ** & 0.626 ** & 0.761 ** & 0.791 ** & 0.795 ** & 0.743 ** & 1.000 \\ \hline \end{tabular}  
* * Correlation is significant at the 0.01 level. RI = resilience improvement.  
\end{table}
Table 4: Pearson correlation result.  
Although all driving variables' coefficients are small except PA and FR, the result should be interpreted carefully, as all driving variables have high correlations with resilience improvement. The high correlations among driving variables indicate that multicollinearity exists and the small coefficients are meaningless. Hence, it is better to discuss the influence of variable combinations from a configuration perspective.