## 4 Results and Discussion
### Prediction Models Using All Factors in the Data  
Further analysis was conducted to test the effect of the data divided according to the classes of retroreflective sheeting on the performance of the models expressed in terms of R\({}^{2}\) (see Table 5). Generally, the R\({}^{2}\) value decreased for the VTI data, from 0.57 when using all the data points to 0.22 for Class 3, while the NMF data R\({}^{2}\) value was approximately the same (0.95 to 0.92). The reason for the decrease in R\({}^{2}\) values was because of the low number of observations in the divided data (a subset of data according to classes) compared with the total datasets which contain all classes. The R\({}^{2}\) values of Class 3 in the VTI data decreased from 0.57 to 0.22 because the age of the reflective sheeting of this class had a maximum of 14 years compared with 36 years for all classes in the dataset. The lower age of Class 3 makes the prediction more difficult because of a lack of information about what happens to retroreflectivity after 14 years. Even models of Class 1 and Class 2 were less accurate, with the prediction difficult for all colors because Class 1 includes no red and green colors while no green color was included in Class 2. The colors were significant in predicting retroreflectivity, so omitting information about some colors is expected to affect the model's performance. All classes in NMF showed a higher R\({}^{2}\) value than for VTI data (see Table 5). The high R\({}^{2}\) values for models fitted on NMF data indicate a linear relationship. The linearity was clearer in NMF data compared with the VTI dataset. This was because the weather conditions, locations, directions, and GPS positions were the same for the retroreflective samples in the NMF data, while in the VTI data, measurements were recorded on different road signs that were mounted in different locations, directions, and GPS positions, and were exposed to different weather conditions. The datasets were further divided according to the classes and colors of the retroreflective sheeting to investigate the effect on the performance of the regression models applied on the divided data, as shown in Table 6.  
Generally, the models for the VTI dataset give higher R\({}^{2}\) values for individual colors compared with the models containing all colors. The higher R\({}^{2}\) value of the VTI data can be explained by the fact that the data contained neither green nor red in some classes, which makes the comparison more reasonable when the data is grouped according to class and color. The R\({}^{2}\) values for the NMF data decreased despite the color being significant to retroreflectivity. Since the NMF data has fewer predictors, removing color and class makes the models less accurate. As previously mentioned, fewer predictors decreases the R\({}^{2}\) value, especially for NMF data that have only six predictors and a low age of five years. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**DATA** & **Predictors** & \begin{tabular}{c} **Class of** \\ **Retroreflection** \\ \end{tabular} & \begin{tabular}{c} **R\({}^{2}\)** \\ \end{tabular} \\ \hline VTI & \begin{tabular}{c} X + Y + Direction + GPSlat + GPSlong \\ + Age + Color \\ \end{tabular} & \begin{tabular}{c} 1 \\ 2 \\ 3 \\ \end{tabular} & \begin{tabular}{c} 0.44 \\ 0.49 \\ 0.22 \\ \end{tabular} \\ \hline NMF & \begin{tabular}{c} X + Y+ \(\beta\) +Age + Color \\ \end{tabular} & \
\begin{tabular}{c} 1 \\ 2 \\ 3 \\ \end{tabular} &
\begin{tabular}{c} 0.94 \\ 0.93 \\ 0.92 \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 5: R\({}^{2}\) values for each class for VTI and NMF data (using logarithmic regression). It was also noticed that logarithmic regression models of the yellow, red, and white colors in NMF data produced relatively higher R\({}^{2}\) values than other colors. These three colors have the highest \(\beta\) among the other colors.