## 3 Results
### Multivariate Analysis  
We performed a multivariate analysis of the items that were significant in the univariate analysis (Table 3). Neither PM2.5 nor any of the ionic components other than SO4\({}^{2-}\) and Mg2+ were included in the analysis because they were highly correlated with PM2.5 or these other ions (as shown in Table 4, there is a strong correlation between Mg2+ and Ca2+ ions, and between NH4\({}^{-}\) and SO4\({}^{2-}\) ions, so Ca2+ and NH4\({}^{-}\) were excluded from the calculation). According to the results of the multivariate analysis, the prediction formula for the prevalence of skin symptoms was as follows: prevalence of skin symptom exacerbations = 0.538 + 0.0017 \(\times\) SO4\({}^{2-}\) + 0.00108 \(\times\) Mg2+. \begin{table}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline  & **PM2.5** & **CL**\({}^{-}\) & **NO3**\({}^{-}\) & **SO4\({}^{2-}\)** & **Na*** & **NH4\({}^{+}\)** & **K*** & **Ca2+** & **Mg2+** \\ \hline PM2.5 & - & & & & & & & & \\ \hline Cl\({}^{-}\) & 0.209 & - & & & & & & \\ \hline NO3\({}^{-}\) & 0.533 & 0.148 & - & & & & & \\ \hline SO4\({}^{2-}\) & 0.554 & \(-\)0.2 & 0.387 & - & & & & \\ \hline Na\({}^{+}\) & 0.212 & 0.129 & 0.071 & 0.416 & - & & & \\ \hline NH4\({}^{+}\) & 0.598 & \(-\)0.157 & 0.665 & 0.919 & 0.22 & - & & \\ \hline K\({}^{+}\) & 0.601 & \(-\)0.285 & 0.384 & 0.721 & 0.188 & 0.753 & - & \\ \hline Ca2+ & 0.594 & 0.592 & 0.458 & 0.025 & 0.416 & 0.231 & 0.065 & - & \\ \hline Mg2+ & 0.647 & 0.422 & 0.393 & 0.215 & 0.297 & 0.179 & 0.143 & 0.815 & - \\ \hline \end{tabular}
\end{table} 
Table 4: Correlation coefficients between each variable. \begin{table}
\begin{tabular}{c c c c c} \hline  & **Unit** & **Mean** & **SD** & **Median** & **Min** & **Max** \\ \hline K\({}^{+}\) & \(\mathrm{\mu g/m^{3}}\) & 0.27 & 0.13 & 0.26 & 0.08 & 0.90 \\ Ca2+ & \(\mathrm{\mu g/m^{3}}\) & 0.01 & 0.01 & 0.01 & 0.004 & 0.059 \\ Mg2+ & \(\mathrm{\mu g/m^{3}}\) & 0.34 & 0.28 & 0.29 & 0.09 & 2.88 \\ \hline \end{tabular}
\end{table} 
Table 2: _Cont._ \begin{table}
\begin{tabular}{c c c} \hline  & **rs** & **P** \\ \hline PM2.5 & 0.3905 ** & 9.50 \(\times\) 10\({}^{-6}\) \\ \hline Cl\({}^{-}\) & 0.0343 & 0.7084 \\ \hline NO3\({}^{-}\) & 0.1014 & 0.2684 \\ \hline SO4\({}^{2-}\) & 0.3263 ** & 0.0003 \\ \hline Na\({}^{+}\) & 0.1525 & 0.095 \\ \hline NH4\({}^{+}\) & 0.3214 ** & 0.0003 \\ \hline K\({}^{+}\) & 0.2292 * & 0.0115 \\ \hline Ca2+ & 0.0651 & 0.4778 \\ \hline Mg2+ & 0.3018 ** & 0.0008 \\ \hline \end{tabular}
\end{table} 
Table 3: Relationship between the daily prevalence of skin symptom exacerbations and the concentration of PM2.5 and its ionic components. Figure 1: Scatter plot of the relationship between the prevalence of daily skin symptoms and the daily mean concentration of PM2.5 and its ionic components. The results shown in parts (**a-e**) of the figure are as follows (all analyses were two-tailed): (**a**) the relationship between the prevalence of skin symptoms and PM2.5, rs = 0.326, \(p\) = 0.0003; (**b**) the relationship between the prevalence of skin symptoms and SO4\({}^{-2}\), rs = 0.391, \(p\) = 9.5 \(\times\) 10\({}^{-6}\); (**c**) the relationship between the prevalence of skin symptoms and NH4\({}^{+}\), rs = 0.321, \(p\) = 0.00032; (**d**) the relationship between the prevalence of skin symptoms and K\({}^{+}\), rs = 0.229, \(p\) = 0.0115; (**e**) the relationship between the prevalence of skin symptoms and Mg2\({}^{+}\), rs = 0.302, \(p\) = 0.0008. PM2.5, particulate matter 2.5. The relationship between the values calculated by this formula and the measured values was statistically significant (n = 121, \(p\) = 0.00026, r = 0.326; Figure 2, Table 5). The prevalence of skin symptoms was calculated by the following formula obtained from multivariate analysis: 0.538 + 0.0017 \(\times\) SO4\({}^{2^{-}}\) + 0.0108 \(\times\) Mg2\({}^{+}\). The relationship between the skin symptoms calculated by this formula and the daily skin symptoms recorded by patients was statistically significant (n = 121, rs = 0.326, \(p\) = 0.00026 [two-tailed]).