## 3 Results and Discussion  
Several studies [28; 32; 33] conclude that \(\log Q\) is the covariable that better explains the noise level, where \(Q\) is the total number of vehicles. This coincides with other studies [34; 35] on noise pollution in close urban areas. In this case, the variable \(\log Q\) seems to be the determinant element for the noise level in the city, and it is a significant covariable in all of the time periods. These covariables have been analyzed separately in each one of the five time periods. However, other variables could have a significant impact in any of the time periods, although less important than the road traffic. This is the reason why the following simple linear model has been adopted for all the time periods:  
\[\mu(x)=\beta_{0}+\beta_{1}\log Q(x), \tag{3}\]  
where \(\beta_{0}\) and \(\beta_{1}\) determine the corresponding offset and slope of the model, respectively. Table 4 gathers the tendency estimations of both parameters and their errors for the data in the five time periods. Once the tendency is adjusted, a first analysis of the spatial structure of the residuals has been conducted. The residuals have been represented graphically in the geographical coordinates (Figure 6) and a contrast test has been performed to check the spatial independence of the observations [30]. The nugget effect (see variogram part of Table 4) can be attributed to measurement errors or spatial sources of variation at smaller distances than the sampling interval (or both). Measurement errors occur due to the inherent error in measuring devices. Natural phenomena can vary spatially over a range of scales (i.e., micro or macro scales). Variation at micro scales smaller than the sampling distances will appear as part of the nugget effect. When looking at the model of a semivariogram, it is noticeable that, at a certain distance from the measurement points of the model, the error levels are higher but bounded (see Figure 7b). The distance where the model first flattens out is known as the range (in this case, the range is related to the arc seconds of the coordinates). The sill is the value where the semivariogram model attains the range (the value on the \(y\)-axis). \begin{table}
\begin{tabular}{c c c c c c c} \hline  & & **Period 1** & **Period 2** & **Period 3** & **Period 4** & **Period 5** \\ \hline \multirow{4}{*}{Tendency} & \(\beta_{0}\) & 53.029 & 60.132 & 54.791 & 53.687 & 52.329 \\  & \(\beta_{0}\)-Std. Error & 12.86 & 11.15 & 6.50 & 5.60 & 10.86 \\  & \(\beta_{1}\) & 5.071 & 2.021 & 4.736 & 5.029 & 4.986 \\  & \(\beta_{1}\)-Std. Error & 0.42 & 0.60 & 0.66 & 0.54 & 0.55 \\ \hline \multirow{4}{*}{Independency Test} & Long & 0.779 & 0.144 & 0.003 & 0.258 & 0.430 \\  & Lat & 0.019 & 0.223 & 0.000 & 0.025 & 0.074 \\  & Long*Lat & 0.256 & 0.025 & 0.000 & 0.410 & 0.375 \\ \hline \multirow{4}{*}{Variogram} & Nugget & 9.359 & 11.357 & 12.670 & 4.069 & 15.676 \\  & Sill & 37.436 & 45.429 & 38.084 & 35.009 & 33.358 \\  & Range (degree) & 0.007 & 0.004 & 0.005 & 0.002 & 0.005 \\ \hline \multirow{4}{*}{Prediction} & MSE (Mean & & & & \\  & Squared & 3.902 & 4.602 & 3.132 & 3.236 & 7.127 \\  & Error).lm & & & & & \\  & MSE.glm & 3.990 & 3.907 & 3.696 & 3.546 & 6.401 \\ \hline \multirow{4}{*}{Cross-Validation (CRV)} & CRV1.glm & \(-\)0.004 & 0.003 & 0.004 & \(-\)0.001 & 0.005 \\  & CRV2.glm & 1.068 & 1.010 & 0.816 & 0.941 & 0.800 \\ \cline{1-1}  & CRV3.glm & 4.664 & 5.348 & 3.755 & 4.589 & 4.218 \\ \hline \end{tabular}
\end{table} 
Table 4: Summary of the spatial-temporal analysis of noise levels. From the \(P\)-values in the independence test shown in Table 3 and the graphics shown in Figure 6, we can say that the residuals are spatially correlated in all the time periods, except for the time period 5 (Figure 6e). The time periods 1 and 4 have a unique dependence in latitude, while periods 2 and 3 are correlated in latitude.