# Laboratory Evaluation of Wear Particle Emissions and
## 3 Results
### Development of the TRWP Emission Estimation Equation Based on Suspended Dust Concentration
#### 3.2.2 Regression Analysis  
The variables used in regression analysis to develop an estimation equation may suffer from multicollinearity issues because dust particles from the same mixture are classified by size. To address this challenge, a multicollinearity analysis was conducted on the selected variables (suspended dust concentrations for PM\({}_{2}\), PM\({}_{5}\), and PM\({}_{10}\)). Multicollinearity refers to the phenomenon in which highly correlated variables are included among variables used in regression analysis, which degrades the estimation precision of regression coefficients. Multicollinearity can be verified using the variance inflation factor (VIF), as shown in Equation (1). The VIF indicates the extent to which one independent variable can be explained by the other variables. In general, a VIF of 10 or higher implies that there is a high multicollinearity. \[\text{VIF}_{i}=\frac{1}{1-R_{i}^{2}}, \tag{1}\]  
where VIF is the variance inflation factor, \(i\) is the result of the selected dependent variable among the independent variables, and \(R^{2}\) is the coefficient of determination. According to the VIF analysis results, PM\({}_{2}\) had a VIF of 5 or less, as shown in Table 5, so multicollinearity issues did not occur. However, the VIF for the suspended dust concentrations for PM\({}_{5}\) and PM\({}_{10}\) was 10 or higher; this result indicates multicollinearity issues. \begin{table}
\begin{tabular}{c c} \hline
**Size of Particulate Matter** & **Coefficient of Determination** \\ \hline PM\({}_{0,3}\) & 0.372 \\ PM\({}_{0,5}\) & 0.002 \\ PM\({}_{1}\) & 0.039 \\ PM\({}_{2}\) & 0.705 \\ PM\({}_{5}\) & 0.983 \\ PM\({}_{10}\) & 0.976 \\ \hline \end{tabular}
\end{table} 
Table 4: R\({}^{2}\) for the relationships between TRWP emissions and suspended dust concentrations by PM size. Figure 12: Relationship between suspended dust concentrations and TRWP emissions. The fact that a dust particle size of PM\({}_{10}\) is commonly used to evaluate suspended dust in the road environment field was considered in this study. Hence, PM\({}_{5}\) was excluded, which has multicollinearity issues, and a multiple regression analysis was conducted using the suspended dust concentrations for PM\({}_{10}\) and PM\({}_{2}\) to develop the TRWP emission estimation equation. The results of the TRWP emission regression analysis using PM\({}_{10}\) and PM\({}_{2}\) showed an adjusted coefficient of determination of 0.9758, indicating a high explanatory power for the estimation equation. However, as shown in Table 6, the regression coefficient for PM\({}_{2}\) was a negative number, and the \(p\)-value was greater than or equal to 0.05, indicating it did not satisfy the significance level. The regression coefficient for PM\({}_{10}\) was a positive number, showing a relationship between general concentration and TRWP emissions. Furthermore, the \(p\)-value was less than or equal to 0.05, indicating it satisfied the significance level. After conducting the correlation analysis and multicollinearity verification and performing the sign verification and significance level determination through the regression analysis, we considered it appropriate to estimate the TRWP emissions based on the suspended dust concentration for PM\({}_{10}\). Table 7 lists the regression analysis results of the suspended dust concentration for PM\({}_{10}\) and the TRWP emissions. The linear regression analysis was conducted using a suspended dust concentration for PM\({}_{10}\), which is the single independent variable, and TRWP emissions, which is the dependent variable. The analysis results yielded a coefficient of determination of 0.9761, demonstrating a high explanatory power for the estimation equation. Moreover, the \(p\)-value was less than or equal to 0.05, which satisfied the significance level. The TRWP emission estimation equation determined through the regression analysis is shown in Equation (2).