## 4 Results and Discussion
### Prediction Models Using All Factors in the Data
As shown in Tables 3 and 4, the logarithmic regression models applied on the datasets that include all factors were more accurate than the linear regression models. The best regression models came from using backward stepwise selection on logarithmic regression models, as shown in Equations (2) and (3). Based on VTI data (R\({}^{2}\) = 0.57):  
\[ \begin{split}\log(1+\text{R}_{\text{A}})=-5.25-1.74\times\text{ X}+8.84\times\text{Y}-0.71\times\text{G}-0.46\times\text{R}+0.05\times\text{W}-0.98 \times\text{Ye}-0.25\\ \times(\text{Dir}/360)+0.12\times\text{lat}-0.05\times\text{Age}+1.39 \times\text{CI2}+1.90\times\text{CI3}\end{split}  \tag{2}\]  
Based on NMF data (R\({}^{2}\) = 0.95):  
\[\log(1+\text{R}_{\text{A}})=1.92+1.47\times\text{X}+0.57\times\text{G}+0.18 \times\text{R}+2.09\times\text{W}+1.51\times\text{Ye}-0.04\times\text{Age}+0.89 \times\text{CI2}+1.89\times\text{CI3} \tag{3}\]  
where:  
\(\text{R}_{\text{A}}\) = The calculated coefficient of retroreflectivity. \(\text{X}\), \(\text{Y}\) = Daylight chromaticity. \(\text{Age}\) = The age of the road sign in years. \(\text{G}\) = A constant must be set to 1 if the color is Green, otherwise set to 0. \(\text{R}\) = A constant must be set to 1 if the color is Red, otherwise set to 0. \(\text{W}\) = A constant must be set to 1 if the color is White, otherwise set to 0. \(\text{Ye}\) = A constant must be set to 1 if the color is Yellow, otherwise set to 0. \(\text{CI2}\) = A constant must be set to 1 if the class is 2, otherwise set to 0. \(\text{CI3}\) = A constant must be set to 1 if the class is 3, otherwise set to 0. \(\text{Dir}\): The compass direction (Direction) in degrees gives the direction that the sign is facing (0, 90, 180, and 270 represent north, east, south, and west, respectively). \(\text{lat}\), long: The coordinates (GPSlat, GPSlong) where the sign is mounted at the geographic coordinate system. The performance of the prediction models in Equations (2) and (3) differs for each dataset because of the differences in the size, age, and placing of the retroreflective sheeting. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Color**} & \multirow{2}{*}{**Class**} & **VTI Data** & **NMF Data** \\ \cline{3-4}  & & **Predictors:** & **Predictors:** \\  & & **X + Y + Direction + GPSlat + GPSlong + Age** & **X + Y + \(\beta\) + Age** \\ \hline \multirow{4}{*}{Blue} & 1 & 0.64 & 0.32 \\ \cline{2-4}  & 2 & 0.97 & 0.36 \\ \cline{2-4}  & 3 & 0.73 & 0.21 \\ \hline \multirow{4}{*}{Green} & 1 & No green in Class 1 & 0.34 \\ \cline{2-4}  & 2 & No green in Class 1 & 0.49 \\ \cline{2-4}  & 3 & 0.71 & 0.23 \\ \hline \multirow{4}{*}{Yellow} & 1 & 0.74 & 0.62 \\ \cline{2-4}  & 2 & 0.99 & 0.44 \\ \cline{2-4}  & 3 & 0.81 & 0.07 \\ \hline \multirow{4}{*}{Red} & 1 & No red in Class 1 & 0.39 \\ \cline{2-4}  & 2 & 0.42 & 0.50 \\ \cline{2-4}  & 3 & 0.97 & 0.63 \\ \hline \multirow{4}{*}{White} & 1 & 0.50 & 0.62 \\ \cline{2-4}  & 2 & 0.98 & 0.12 \\ \cline{1-1} \cline{2-4}  & 3 & 0.74 & 0.50 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: R\({}^{2}\) values for each color and class for VTI and NMF data (using logarithmic regression). The logarithmic regression models on the NMF data showed a higher R\({}^{2}\) value than for the VTI data because the NMF data were collected from samples that have the same size and are exposed to the same conditions. Age has a negative coefficient in Equations (2) and (3), confirming that the retroreflectivity decreases (by 4-5%) for a unit increase in age of the road sign, given all other factors in the model are held constant. There is a big difference in the age of traffic signs included in the two datasets. While the age of traffic signs in the NMF data is just five years, the age of the traffic signs in the VTI dataset has a maximum of 36 years. Referring to Equations (2) and (3), the VTI dataset gives a negative X coordinate (\(-1.74\)), while the coefficient of the NMF dataset is positive (\(+1.47\)).