## 3 Results and Discussion
### Partial Correlation Matrix among PMs of Gangneung (G) and PMs of Beijing (B)
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Period**} & \multicolumn{2}{c}{**Multi-Correlation Coefficient**} & \multicolumn{2}{c}{**Predictive Regression Equation**} \\  & 0.983 & & \(\text{PM}_{10}(\text{G})=\) & \(3.353\times\text{PM}_{2.5}(\text{G})-2.708\times\text{PM}_{1}(\text{G})\) \\  & 0.983 & & \(+\) 0.601 \(\times\text{T}(\text{G})-1.240\times\text{W}(\text{G})+0.009\times\text{RH}( \text{G})\) \\  & & & \(-\) 0.006 \(\times\text{PM}_{10}(\text{G})+0.002\times\text{PM}_{2.5}(\text{B})-2.206\) \\
18/03/2015 to 21/03/2015 to 21/03/2015 & 0.998 & & \(-\) 0.211 \(\times\text{PM}_{10}(\text{G})+0.917\times\text{PM}_{1}(\text{G})\) \\  & 0.998 & & \(-\) 0.245 \(\times\text{T}(\text{G})+0.269\times\text{W}(\text{G})-0.035\times\text{RH}( \text{G})\) \\  & & & \(+\) 0.006 \(\times\text{PM}_{10}(\text{B})-0.007\times\text{PM}_{2.5}(\text{B})+4.638\) \\  & & & \(-\) 0.193 \(\times\text{PM}_{10}(\text{G})+1.038\times\text{PM}_{2.5}(\text{G})\) \\  & 0.258 \(\times\text{T}(\text{G})-0.240\times\text{W}(\text{G})+0.049\times\text{RH}( \text{G})\) \\  & & & \(-\) 0.005 \(\times\text{PM}_{10}(\text{B})+0.006\times\text{PM}_{2.5}(\text{B})-5.710\) \\ \hline  & 0.916 & \(\text{PM}_{10}(\text{G})=\) & \(3.560\times\text{PM}_{2.5}(\text{G})-3.114\times\text{PM}_{1}(\text{G})\) \\  & 0.916 & & \(-\) 0.914 \(\times\text{T}(\text{G})+4.444\times\text{W}(\text{G})-0.360\times\text{RH}( \text{G})\) \\  & & & \(+\) 0.082 \(\times\text{PM}_{10}(\text{B})-0.252\times\text{PM}_{2.5}(\text{B})+42.893\) \\
21/03/2015 to 23/03/2015 & 0.998 & & \(0.047\times\text{PM}_{10}(\text{G})+1.166\times\text{PM}_{1}(\text{G})\) \\  & 0.998 & & \(-\) 0.003 \(\times\text{T}(\text{G})-0.525\times\text{W}(\text{G})-0.009\times\text{RH}( \text{G})\) \\  & & & \(-\) 0.001 \(\times\text{PM}_{10}(\text{B})-0.019\times\text{PM}_{2.5}(\text{B})+7.359\) \\  & 0.998 & & \(-\) 0.030 \(\times\text{PM}_{10}(\text{G})+0.842\times\text{PM}_{2.5}(\text{G})\) \\  & & & \(+\) 0.042 \(\times\text{T}(\text{G})+0.406\times\text{W}(\text{G})+0.009\times\text{RH}( \text{G})\) \\  & 0.001 \(\times\text{PM}_{10}(\text{B})+0.020\times\text{PM}_{2.5}(\text{B})-6.874\) \\ \hline  & 0.941 & \(\text{PM}_{10}(\text{G})=\) & \(6.841\times\text{PM}_{2.5}(\text{G})-6.102\times\text{PM}_{1}(\text{G})\) \\  & 0.941 & & \(-\) 0.548 \(\times\text{T}(\text{G})+1.859\times\text{W}(\text{G})-0.433\times\text{RH}( \text{G})\) \\  & & & \(-\) 0.008 \(\times\text{PM}_{10}(\text{B})+0.002\times\text{PM}_{2.5}(\text{B})-1.628\) \\
23/03/2015 to 27/03/2015 & 0.998 & & \(0.090\times\text{PM}_{10}(\text{G})+0.946\times\text{PM}_{1}(\text{G})\) \\  & & & \(+\) 0.061 \(\times\text{T}(\text{G})-0.182\times\text{W}(\text{G})+0.044\times\text{RH}( \text{G})\) \\  & & & \(+\) 0.002 \(\times\text{PM}_{10}(\text{B})-0.001\times\text{PM}_{2.5}(\text{B})+1.747\) \\  & 0.998 & & \(-\) 0.088 \(\times\text{PM}_{10}(\text{G})+1.042\times\text{PM}_{2.5}(\text{G})\) \\  & & & \(-\) 0.060 \(\times\text{T}(\text{G})+0.185\times\text{W}(\text{G})-0.043\times\text{RH}( \text{G})\) \\  & 0.954 & & \(-\) 0.054 \(\times\text{T}(\text{G})+3.456\times\text{W}(\text{G})-0.112\times\text{RH}( \text{G})\) \\  & & & \(+\) 0.039 \(\times\text{PM}_{10}(\text{B})-0.018\times\text{PM}_{2.5}(\text{B})-12.128\) \\
18/03/2015 to 27/03/2015 & 0.998 & & \(0.104\times\text{PM}_{10}(\text{G})+1.059\times\text{PM}_{1}(\text{G})\) \\  & 0.003 \(\times\text{T}(\text{G})-0.328\times\text{W}(\text{G})+0.019\times\text{RH}( \text{G})\) \\  & & & \(+\) 0.005 \(\times\text{PM}_{10}(\text{B})-0.001\times\text{PM}_{2.5}(\text{B})+1.350\) \\  & & & \(-\) 0.088 \(\times\text{PM}_{10}(\text{G})+0.924\times\text{PM}_{2.5}(\text{G})\) \\  & & & \(+\) 0.006 \(\times\text{T}(\text{G})+0.268\times\text{W}(\text{G})-0.014\times\text{RH}( \text{G})\) \\  & & & \(-\) 0.005 \(\times\text{PM}_{10}(\text{B})+0.010\times\text{PM}_{2.5}(\text{B})-1.246\) \\ \hline \hline \end{tabular}
\end{table}