## 4 Results and Discussion
### Prediction Models Using Factors That Can Be Collected without Instruments
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Colors Included in the Model**} & \multirow{2}{*}{**Classes Included in the Models**} & **VTI Data** & **NMF Data** \\ \cline{3-4}  & & **Number of Observations** & **Number of Observations** \\ \hline \multirow{4}{*}{All(blue + green + yellow + red + white)} & All (1 + 2 + 3) & 1544 & 710 \\ \cline{2-4}  & All (1 + 2 + 3) & 154 & 603 & 154 \\ \cline{2-4}  & All (1 + 2 + 3) & 258 & 191 \\ \cline{2-4}  & All (1 + 2 + 3) & 683 & 365 \\ \hline \multirow{4}{*}{All(blue + green + yellow + red + white)} & 1 & 196 & 32 \\ \cline{2-4}  & All (1 + 2 + 3) & 98 & 42 \\ \cline{2-4}  & All (1 + 2 + 3) & 117 & 78 \\ \hline \multirow{4}{*}{Green} & 1 & - & 32 \\ \cline{2-4}  & All (1 + 2 + 3) & 42 \\ \cline{2-4}  & All (1 + 2 + 3) & 42 \\ \hline \multirow{4}{*}{Yellow} & 1 & 205 & 32 \\ \cline{2-4}  & All (1 + 2 + 3) & 24 \\ \cline{2-4}  & All (1 + 2 + 3) & 186 & 47 \\ \hline \multirow{4}{*}{Red} & 1 & - & 26 \\ \cline{2-4}  & All (1 + 2 + 3) & 24 \\ \cline{2-4}  & All (1 + 2 + 3) & 24 \\ \hline \multirow{4}{*}{White} & 1 & 202 & 32 \\ \cline{2-4}  & All (1 + 2 + 3) & 24 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: The number of observations for divided data. can be checked using diagnostic plots [19]. The diagnostic plots of the logarithmic models (Figures 6 and 7) showed that:  
* The Residuals vs. Fitted values plot shows an almost horizontal line around the zero value. This indicates a linearity relationship between retroreflectivity and the predictors for the VTI and NMF data. * The residuals are more normally distributed in the NMF data because the Normal Q-Q plot shows that the residual points almost follow the straight dashed line. However, the VTI data residuals follow the dashed line only in the middle part of the plot. * The Scale-Location plot that was used to check the homogeneity of variance of the residuals (homoscedasticity) gives no indications of heteroscedasticity problems. A horizontal line with equally spread points is expected to indicate good homoscedasticity, and this is the case with both the VTI and NMF data. * The Residuals vs. Leverage plots indicate the presence of some outliers in both datasets. The performance in terms of the R\({}^{2}\) values of the two models that were suggested in Equations (4) and (5) are almost equal to those of the models in Equations (2) and (3). This means that predictors requiring instruments to measure them can be excluded from the predicting models without affecting the models' performance. In summary, the models described in Equations (4) and (5) can be used to predict retroreflectivity and provide an accurate, safe, and unexpressive method. The regression models from studies as early as 2011 produced R\({}^{2}\) values ranging from 0.10 to 0.30 [12], while a 2017 study had R\({}^{2}\) values ranging from 0.52 to 0.57 [1]. However, the regression models in Equations (4) and (5) of this study showed a better fit with the data than previous models, with R\({}^{2}\) values of 0.50 and 0.95. Figure 6: Checking the assumptions for logarithmic regression of the VTI data.