# An Analysis of Spatial Variation in Human Impact on Forest Ecological Functions
## 3 Results
### Impact of Human Activities on FEF  
A multiple covariance test is conducted with the help of IBM SPSS Statistics version 27.0 to avoid pseudo-regression. The results show that the variance inflation factor (VIF) of each variable is less than 5 (Table 3), indicating that the variables are independent of each other and meet the regression requirements. We also standardize all the variables to ensure the robustness of the model and the credibility of the results. After that, we apply MLR and GWR models to regress the influencing factors of forest ecological functions, respectively. The results of regression and the model fitting are shown in Table 3.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Variable**} & \multirow{2}{*}{**MLR**} & \multicolumn{6}{c}{**GWR**} \\ \cline{3-8}  & & & **Min** & **Max** & \
\begin{tabular}{c} **Lwr** \\ **Quartile** \\ \end{tabular} & **Medium** &
\begin{tabular}{c} **Upr** \\ **Quartile** \\ \end{tabular} & **Mean** & **VIF** \\ \hline ECO & \(-0.103\)* & \(-0.737\) & \(0.171\) & \(-0.117\) & \(-0.073\) & \(-0.026\) & \(-0.071\) & 3.047 \\ AGRI & \(-0.174\)*** & \(-0.354\) & \(0.119\) & \(-0.166\) & \(-0.118\) & \(-0.073\) & \(-0.123\) & 2.903 \\ INDS & \(0.021\) & \(-0.139\) & \(0.233\) & \(-0.014\) & \(0.028\) & \(0.055\) & \(0.015\) & 2.251 \\ PDS & \(-0.035\) & \(-0.754\) & \(1.491\) & \(-0.117\) & \(-0.079\) & \(0.003\) & \(-0.063\) & 2.265 \\ URB & \(-0.012\) & \(-0.201\) & \(0.314\) & \(-0.047\) & \(-0.001\) & \(0.030\) & \(-0.003\) & 4.657 \\ PDUC & \(0.011\)* & \(-0.862\) & \(0.317\) & \(-0.038\) & \(-0.005\) & \(0.073\) & 0.006 & 2.423 \\ LIVE & \(0.018\) & \(-0.595\) & \(0.263\) & \(0.043\) & \(0.094\) & \(0.126\) & 0.075 & 4.142 \\ PROT & \(0.031\) & \(-0.087\) & \(0.355\) & \(-0.038\) & \(-0.005\) & \(0.123\) & 0.047 & 1.117 \\ TEMP & \(0.504\)*** & \(-0.801\) & \(0.892\) & \(0.224\) & \(0.368\) & \(0.571\) & 0.378 & 2.029 \\ PREC & \(0.299\)*** & \(-0.089\) & \(0.618\) & \(0.161\) & \(0.296\) & \(0.374\) & 0.270 & 1.343 \\ ELEV & \(0.386\)* & \(-1.257\) & \(1.777\) & \(0.249\) & \(0.403\) & \(0.932\) & 0.587 & 1.139 \\ SLOP & \(0.438\)** & \(-0.037\) & \(0.313\) & \(0.096\) & \(0.194\) & \(0.258\) & 0.175 & 2.313 \\ SOIL & \(0.000\) & \(-0.425\) & \(0.145\) & \(-0.048\) & \(0.021\) & \(0.083\) & 0.07 & 1.328 \\ AIC & \(-749.032\) & & & & \(-797.521\) & & & - \\ R\({}_{\rm adj}^{2}\) & \(0.467\) & & & \(0.692\) & & & - \\ \hline \hline \end{tabular} Note: **, **, and * indicate significance at 0.01, 0.05, and 0.1 levels, respectively. Acronyms are defined in Table 2.  
\end{table}
Table 3: Results of MLR and GWR models and comparison of their performance.  
The results of the MLR regression show the overall impact of human activities on the FEF. Figure 3 exhibits that residual values are located around the diagonal line, indicating that residual values in this model follow a normal distribution, which displays the correctness of the performed regression. It can be seen that three of the eight human activity factors we selected have significant effects on FEF. Economic and agricultural development, growth in population density, and accelerated urbanization mostly inhibit FEF, whereas the development of secondary industry, the increasing proportion of productive land and living land and forest protection contribute to FEF. Since the GWR regression shows a higher value of \(\mathrm{R}^{2}_{\mathrm{adj}}\) (0.692) and a smaller AIC (\(-\)797.521) than MLR regression, we believe that the GWR model better contributes to elucidating spatial variations in the influencing factors we analyzed. The local \(\mathrm{R}^{2}\) values can be seen in Appendix A Figure A1, which shows the GWR model fits better than OLS model in most of the counties. Therefore, the results of GWR regression will act as the basis for the following discussion.