## 3 Results and Discussion
### PM\({}_{2.5}\) Prediction Model for Administrative Districts  
The PM\({}_{2.5}\) prediction model for AD, was developed in the same way as the NW PM\({}_{2.5}\) prediction model. As shown in Table 10, based on a significance level of 0.05, the two main effects of the hidden layer layout and the threshold were significant, and they were also the most significant among all the interaction effects. Unlike the NW analysis, the month factor was not clearly significant in the ANOVA. As with the NW prediction model, the model with the month factor had higher overall R-squared than the model without the month factor (Figure 8). Although it is not as sharp as the NW model in Figure 6, the in-sample R-squared value decreased as the threshold increased. As the number of nodes in the hidden layer layout decreased and the threshold increased, Figure 8 describes that the deviation between the in-sample and out-of-sample R-squared values decreased, and the overfitting problem also reduced. Therefore, the model with the highest average R-squared value and a less than 10% difference between in-sample and out-of-sample R-squared values was selected as the optimal PM\({}_{2.5}\) prediction model. Thus, when the month factor was included, the number of nodes in the hidden layer layout was 12, and the threshold was 0.05. Table 11 shows the R-squared and absolute errors in n \(\sigma\) of the optimal PM\({}_{2.5}\) prediction model for AD (month factor: included, hidden layer layout: 6 \(\times\) 6, threshold: 0.05). As shown in Figure 8 and Table 5, the accuracy of the PM\({}_{2.5}\) prediction model for AD is slightly lower than that of the PM\({}_{2.5}\) NW prediction model. R-squared of PM\({}_{2.5}\) prediction model without weather forecasting for AD are 0.65 (in-sample) and 0.55 (out-of-sample), and the absolute error in 1 \(\sigma\) is 88% and 84%, respectively. Assuming that the weather prediction is accurate, if the meteorological factor on the forecasting day is used instead of data from the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Factor** & **Degree of Freedom** & **Sum of Squares** & **Mean Squares** & **F Value** & **Pr \(\circ\)P)** \\ \hline Month Factor & 1 & 3.56 \(\times\) 10\({}^{-5}\) & 3.56 \(\times\) 10\({}^{-5}\) & 0.250 \(\times\) 10\({}^{-1}\) & 6.27 \(\times\) 10\({}^{-1}\) \\ Hidden Layer Layout & 1 & 6.55 \(\times\) 10\({}^{-3}\) & 6.55 \(\times\) 10\({}^{-3}\) & 46.11 & 2.99 \(\times\) 10\({}^{-5}\) \\ Threshold & 1 & 2.88 \(\times\) 10\({}^{-3}\) & 2.88 \(\times\) 10\({}^{-3}\) & 20.30 & 8.94 \(\times\) 10\({}^{-4}\) \\ Month Factor:Hidden Layer Layout & 1 & 2.09 \(\times\) 10\({}^{-4}\) & 2.09 \(\times\) 10\({}^{-3}\) & 1.47 & 2.51 \(\times\) 10\({}^{-1}\) \\ Month Factor:Threshold & 1 & 7.40 \(\times\) 10\({}^{-6}\) & 7.40 \(\times\) 10\({}^{-6}\) & 5.21 \(\times\) 10\({}^{-2}\) & 8.24 \(\times\) 10\({}^{-1}\) \\ Hidden Layer Layout:Threshold & 1 & 3.79 \(\times\) 10\({}^{-3}\) & 3.79 \(\times\) 10\({}^{-3}\) & 26.70 & 3.10 \(\times\) 10\({}^{-4}\) \\ Residuals & 11 & 1.56 \(\times\) 10\({}^{-3}\) & 1.42 \(\times\) 10\({}^{-4}\) & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 10: ANOVA table of PM\({}_{2.5}\) prediction model for administrative districts. Figure 8: R-squared for administrative district model: (**a**) excluding month factor and (**b**) including month factor. previous day, The R squared increased from 0.65 to 0.73 for in-sample and from 0.55 to 0.65 for out-of-sample. The accuracy of the NW PM\({}_{2.5}\) prediction model can be improved with high accuracy weather forecasting. Figure 9 presents the predicted and measured values of the optimal PM\({}_{2.5}\) prediction model for the AD. PM\({}_{2.5}\) in each region is accurately predicted without considering regional variables. Figure 9b has a slightly smaller difference between the predicted and measured values than Figure 9a. In future studies, a regional variable should be considered or a regional model should be developed separately to further improve the predictive power of the model.