## 4 Results and Discussion
### Prediction Models Using Factors That Can Be Collected without Instruments
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{3}{*}{**Color**} & \multirow{3}{*}{**Class**} & \multicolumn{3}{c}{**VTI Data**} & \multicolumn{2}{c}{**NMF Data**} \\ \cline{3-6}  & & \multicolumn{2}{c}{**Predictors:**} & \multicolumn{2}{c}{**Predictors:**} \\  & & **Age + Direction + GPS Position** & \multicolumn{2}{c}{**Age**} \\ \cline{3-6}  & \multicolumn{2}{c}{**Linear Regression**} & \multicolumn{2}{c}{**Logarithmic Regression**} & \multicolumn{2}{c}{**Linear Regression**} & \multicolumn{2}{c}{**Logarithmic Regression**} \\ \hline \multirow{3}{*}{Blue} & 1 & 0.31 & 0.25 & 0.10 & 0.12 \\ \cline{2-6}  & 2 & 0.02 & 0.01 & 0.22 & 0.29 \\ \cline{2-6}  & 3 & 0.02 & 0.02 & 0.10 & 0.10 \\ \hline \multirow{3}{*}{Green} & 1 & - & - & 0.09 & 0.12 \\ \cline{2-6}  & 2 & - & - & 0.13 & 0.09 \\ \cline{2-6}  & 3 & 0.04 & 0.04 & 0.09 & 0.10 \\ \hline \multirow{3}{*}{Yellow} & 1 & 0.57 & 0.58 & 0.07 & 0.06 \\ \cline{2-6}  & 2 & 0.00 & 0.01 & 0.05 & 0.06 \\ \cline{2-6}  & 3 & 0.03 & 0.04 & 0.04 & 0.06 \\ \hline \multirow{3}{*}{Red} & 1 & - & - & 0.08 & 0.07 \\ \cline{2-6}  & 2 & 0.01 & 0.06 & 0.11 & 0.11 \\ \cline{2-6}  & 3 & 0.04 & 0.03 & 0.08 & 0.09 \\ \hline \multirow{3}{*}{White} & 1 & 0.38 & 0.24 & 0.03 & 0.03 \\ \cline{2-6}  & 2 & 0.19 & 0.13 & 0.06 & 0.05 \\ \cline{1-1} \cline{2-6}  & 3 & 0.06 & 0.05 & 0.03 & 0.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: R\({}^{2}\) values for VTI and NMF regression models for each color and class. Six predictors can be used in Equation (4) to predict retroreflectivity: the class of the retroreflective sheeting, the color of the sign, the direction of the sign, the GPS latitude of the sign, the GPS longitude of the sign, and the age of the sign. These predictors can be easily collected without the need for expensive measuring instruments. Three predictors can be used in Equation (5) to predict retroreflectivity: the class of the retroreflective sheeting, the color of the sign, and the age of the sign. The two models described in Equations (4) and (5) give a different predictive performance in terms of R\({}^{2}\) values, which are 0.50 and 0.95 for prediction models based on the VTI and NMF datasets, respectively. The two datasets differ in size and the age, size, and placing of the tested sheeting in each dataset are different, explaining why the performance of the prediction models differs for each dataset. Age has a negative coefficient in Equations (4) and (5), confirming that 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. The negative coefficient (\(-0.26\)) in Equation (4) for the direction of the road indicates that direction is negatively correlated with RA and that retroreflectivity decreases (by 26%) when the azimuth angle of the road traffic sign increases (by one unit). In particular, the road signs that faces south and west (directions of 180 and 270 degrees from north) fade faster than signs facing north and east (directions of 0 and 90 degrees) and need to be replaced more often. This conclusion is supported by the fact that solar radiation can affect road signs negatively. Four assumptions are necessary so that the regression model can be applied for hypothesis testing, confidence intervals, and prediction [20]. The assumptions of a linearity relationship, homogeneity of variance, uncorrelated errors, and normally distributed errors