## 3 Results and Discussion
### PM\({}_{2.5}\) Prediction Model for Nationwide  
According to the factor levels in Table 2, 18 prediction models were developed NW. Table 8 shows the analysis of variance (ANOVA) table that statistically explains the factorial design experiment results. The response variable in this table is the R-squared of the out-of-sample. Based on a significance level of 0.05, all main effects (hidden layer layout, month, and threshold) affected R-squared. Two interaction effects (month factor and hidden layer layout, and hidden layer layout and threshold) also affected R-squared. Therefore, three factors affected the predictive model. This shows that it is appropriate to find the optimal model according to level change. Figure 6a,b show in-sample/out-of-sample R-squared of the 18 prediction models developed according to factorial design, respectively. The higher the R-squared value was, the better the predictive ability of the model was. However, to avoid overfitting, the difference in R-squared between in-sample and out-of-sample should be minimal. Thus, to prevent overfitting, the model with a high average R-squared (average R-squared for in-sample and out-of-sample) was selected as the optimal model among the models in which the in-sample and out-of-sample R-squared differed within 10%. Using the month factor showed higher R-squared, and in-sample R-squared decreased as the threshold increased. However, if the threshold increased from 0.01 to 0.05 or 0.1, the deviation of R-squared between in-sample \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & z1 & z2 & z3 & z4 & z5 & z6 & zv1 & zv2 & zv3 & zv4 & zv5 & zv6 & y \\ \hline
**z1** & **1.00** & **0.56** & \(-0.22\) & \(-0.80\) & **0.24** & \(-0.39\) & \(-0.31\) & \(-0.30\) & \(-0.32\) & \(-0.25\) & **0.22** & \(-0.24\) & \(-0.31\) \\
**z2** & & **1.00** & \(-0.25\) & \(-0.51\) & **0.48** & \(-0.14\) & \(-0.60\) & \(-0.60\) & \(-0.16\) & \(-0.03\) & **0.24** & \(-0.09\) & \(-0.21\) \\
**z3** & & & **1.00** & \(-0.08\) & **0.11** & **0.19** & \(-0.18\) & **0.07** & **0.87** & **0.53** & \(0.00\) & **0.14** & \(-0.32\) \\
**z4** & & & & **1.00** & \(-0.30\) & **0.25** & **0.39** & **0.24** & \(0.03\) & \(-0.03\) & \(-0.19\) & **0.13** & **0.29** \\
**z5** & & & & & **1.00** & \(-0.03\) & **\(-0.36\)** & \(-0.34\) & **0.21** & **0.29** & **0.70** & \(-0.01\) & \(-0.26\) \\
**z6** & & & & & **1.00** & \(0.02\) & **0.08** & **0.23** & **0.07** & \(-0.04\) & **0.84** & **0.05** \\
**zv1** & & & & & & **1.00** & **0.63** & \(-0.14\) & \(-0.02\) & \(-0.17\) & 0.01 & **0.40** \\
**zv2** & & & & & & & **1.00** & 0.03 & **0.06** & \(-0.20\) & **0.05** & **0.30** \\
**zv3** & & & & & & & & **1.00** & **0.60** & \(0.03\) & **0.16** & \(-0.27\) \\
**zv4** & & & & & & & & & **1.00** & 0.04 & 0.03 & \(-0.07\) \\
**zv5** & & & & & & & & & & **1.00** & \(-0.02\) & \(-0.13\) \\
**zv6** & & & & & & & & & & & **1.00** & \(0.02\) \\ \hline \hline \end{tabular} Bold character represents significant correlation with significant level 0.05.  
\end{table} 
Table 7: Correlations among next-day PM\({}_{2.5}\) levels and meteorological factors (nationwide daily average and variance). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Factor** & **Degree of Freedom** & **Sum of Squares** & **Mean Squares** & **F Value** & **Pr(F-F)** \\ \hline Month & 1 & 0.011243 & 0.011243 & 17.37643 & 0.014048 \\ Hidden Layer Layout & 2 & 0.05415 & 0.027075 & 41.84383 & 0.002081 \\ Threshold & 2 & 0.224784 & 0.112392 & 173.6985 & 0.00013 \\ Month Factor. & 2 & 0.001712 & 0.000856 & 1.322687 & 0.362311 \\ Hidden Layer Layout & 2 & 0.029913 & 0.014957 & 23.11483 & 0.006342 \\ Hidden Layer Layout: Threshold & 4 & 0.148298 & 0.037075 & 57.29761 & 0.000873 \\ Residuals & 4 & 0.002588 & 0.000647 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 8: ANOVA table of nationwide PM\({}_{2.5}\) prediction model. and out-of-sample decreased, thereby reducing the overfitting problem.