# Multivariate Regression Modeling for Coastal Urban Air Quality Estimates
## 3 Results
### Definition of Variables in the Multivariate Regression Model
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Period** & \begin{tabular}{c} **Multi-Correlation** \\ **Coefficient (r)** \\ \end{tabular} & \multicolumn{2}{c}{**Multivariate Predictive Regression Equation**} \\ \hline  & 0.957 & PM10\_K(N) & = & \begin{tabular}{c} \(0.559\times\) PM10\_K\(-\) \(0.175\times\) PM2\_5\_K + 2.362 \(\times\) \\ TEMP\_K \(-\) \(1.355\times\) WIND\_K \(-\) \(0.477\times\) RH\_K \\ \(-\) 2.982 \(\times\) SO\_2\_K + 0.162 \(\times\) CO\_K \(-\) 0.143 \(\times\) O\_3\_K + \\ 0.304 \(\times\) NO\_2\_K + 0.036 \(\times\) PM10\_C \\ \(-\) 0.036 \(\times\) PM2\_5\_C + 0.340 \(\times\) SO\_2\_C \(-\) 0.064 \(\times\) \\ CO\_C \(-\) 0.500 \(\times\) O\_3\_C \(-\) 0.148 \(\times\) NO\_2\_C + 87.948 \\ \hline  & 0.906 & PM\_2\_5\_K(N) & = & \begin{tabular}{c} \(0.122\times\) PM10\_K + 0.452 \(\times\) PM2\_5\_K - 0.164 \(\times\) \\ TEMP\_K + 0.291 \(\times\) WIND\_K + 0.204 \(\times\) RH\_K \\ \(-\) 0.257 \(\times\) SO\_2\_K + 0.148 \(\times\) CO\_K + 0.526 \(\times\) O\_3\_K + \\ 0.565 \(\times\) NO\_2\_K + 0.002 \(\times\) RH\_10\_C \\ \(-\) 0.008 \(\times\) PM2\_5\_C \(-\) 0.075 \(\times\) SO\_2\_C + 0.013 \(\times\) \\ CO\_C + 0.005 \(\times\) O\_3\_C + 0.006 \(\times\) NO\_2\_C \(-\) 37.838 \\ \hline  & 0.886 & NO\_2\_K(N) & = & \begin{tabular}{c} \(0.001\times\) PM10\_K \(-\) 0.058 \(\times\) PM2\_5\_K \(-\) 0.332 \(\times\) \\ TEMP\_K \(-\) \(1.788\times\) WIND\_K + 0.194 \(\times\) RH\_K \\ \(+\) 0.407 \(\times\) SO\_2\_K \(-\) 0.016 \(\times\) CO\_K + 0.156 \(\times\) O\_3\_K + \\ 0.784 \(\times\) NO\_2\_K + 0.001 \(\times\) PM10\_C \\ \(-\) 0.019 \(\times\) PM2\_5\_C \(-\) 0.070 \(\times\) SO\_2\_C \(-\) 0.006 \(\times\) \\ CO\_C + 0.124 \(\times\) O\_3\_C + 0.153 \(\times\) NO\_2\_C \(-\) 19.762 \\ \hline  & 0.795 & SO\_2\_K(N) & = & \begin{tabular}{c} \(-0.013\times\) PM10\_K \(-\) 0.012 \(\times\) PM2\_5\_K + 0.196 \(\times\) \\ TEMP\_K \(-\) 0.415 \(\times\) WIND\_K + 0.030 \(\times\) RH\_K \\ \(+\) 0.521 \(\times\) SO\_2\_K + 0.009 \(\times\) CO\_K \(-\) 0.040 \(\times\) O\_3\_K \\ 0.065 \(\times\) NO\_2\_K \(-\) 0.007 \(\times\) PM10\_C \\ \(+\) 0.003 \(\times\) PM2\_5\_C + 0.021 \(\times\) SO\_2\_C \(-\) 0.001 \(\times\) CO\_C \\ \(-\) 0.001 \(\times\) O\_3\_C + 0.016 \(\times\) NO\_2\_C + 1.862 \\ \hline  & 0.932 & O\_3\_K(N) & = & \
\begin{tabular}{c} \(-0.033\times\) PM10\_K \(+\) 0.012 \(\times\) PM2\_5\_K + 1.353 \(\times\) \\ TEMP\_K \(-\) \(+\) 2.838 \(\times\) WIND\_K \(-\) 0.218 \(\times\) RH\_K \\ \(+\) 0.111 \(\times\) SO\_2\_K + 0.043 \(\times\) CO\_K + 0.564 \(\times\) O\_3\_K \(-\) \\ 0.221 \(\times\) NO\_2\_K + 0.001 \(\times\) PM10\_C \\ \(+\) 0.022 \(\times\) PM2\_5\_C + 0.183 \(\times\) SO\_2\_C + 0.001 \(\times\) CO\_C \\ \(-\) 0.172 \(\times\) O\_3\_C \(-\) 0.182 \(\times\) NO\_2\_C + 26.519 \\ \hline  & 0.864 & CO\_K(N) & = &
\begin{tabular}{c} \(-0.033\times\) PM10\_K \(+\) 0.423 \(\times\) PM2\_5\_K + 0.141 \(\times\) \\ TEMP\_K + 1.200 \(\times\) WIND\_K \(+\) 0.235 \(\times\) RH\_K \\ \(-\) 0.412 \(\times\) SO\_2\_K + 0.372 \(\times\) CO\_K \(-\) 1.404 \(\times\) O\_3\_K \\ \(-\) 1.510 \(\times\) NO\_2\_K + 0.073 \(\times\) PM10\_C \\ \(-\) 0.096 \(\times\) PM2\_5\_C \(-\) 0.056 \(\times\) SO\_2\_C \(-\) 0.068) \(\times\) CO\_C + 0.025 \(\times\) O\_3\_C + 0.221 \(\times\) NO\_2\_C + 67.539 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Multivariate correlation coefficients and predictive regression equations for real-time PM10\_K(N), PM2\_5\_K(N), SO\_2\_K(N), CO\_K(N), O\_3\_K(N) and NO\_2\_K(N) values at Kangnung, Korea (K) affected by meteorological parameters associated with the PM and gases in Beijing, China (C) before the Yellow Sand event, 2015. Multiple correlation coefficients among the real-time predicted PM10_K, PM25_K, SO2_K, CO_K, O3_K and NO2_K values were in the range of 0.795 to 0.982.