## 3 Results
### GAM Analysis Results  
As mentioned earlier, the GAM analysis provides deeper insights than spatial econometric analysis alone. It enhances interpretability and offers a novel approach for deriving policy implications. \begin{table}
\begin{tabular}{c l c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Whole Region (n = 462)**} \\ \hline  & **Variables** & \multicolumn{2}{c}{**Short-Run Effect**} & \multicolumn{2}{c}{**Z-Stat**} & \multicolumn{2}{c}{**Long-Run Effect**} & \multicolumn{2}{c}{**Z-Stat**} \\ \hline  & LnGPPpc & \(-2.012\) & ** & \(-2.04\) & \(-1.856\) & ** & \(-1.98\) \\  & LnGPPpc\({}^{2}\) & \(0.097\) & ** & \(2.44\) & \(0.090\) & ** & \(2.35\) \\ Direct & LnPop\_dens & \(6.444\) & ** & \(2.08\) & \(5.943\) & ** & \(2.10\) \\  & LnRoaddens & \(0.017\) & & \(1.09\) & \(0.016\) & & \(1.11\) \\  & COVID & \(0.006\) & & \(0.84\) & \(0.005\) & & \(0.84\) \\ \hline  & LnGPPpc & \(-0.701\) & & \(-1.15\) & \(-0.582\) & & \(-1.11\) \\  & LnGPPpc\({}^{2}\) & \(0.034\) & & \(1.23\) & \(0.028\) & & \(1.19\) \\ Indirect & LnPop\_dens & \(2.246\) & & \(1.37\) & \(1.864\) & & \(1.35\) \\  & LnRoaddens & \(0.006\) & & \(0.89\) & \(0.005\) & & \(0.87\) \\  & COVID & \(0.002\) & & \(0.66\) & \(0.002\) & & \(0.67\) \\ \hline  & LnGPPpc & \(-2.713\) & * & \(-1.87\) & \(-2.438\) & * & \(-1.82\) \\  & LnGPPpc\({}^{2}\) & \(0.131\) & ** & \(2.19\) & \(0.118\) & ** & \(2.11\) \\ Total & LnPop\_dens & \(8.690\) & ** & \(2.12\) & \(7.801\) & ** & \(2.13\) \\  & LnRoaddens & \(0.023\) & & \(1.06\) & \(0.021\) & & \(1.09\) \\  & COVID & \(0.008\) & & \(0.80\) & \(0.007\) & & \(0.81\) \\ \hline  & \multicolumn{6}{c}{Note: * \(p<0.10\), ** \(p<0.05\).} \\ \end{tabular}
\end{table} 
Table 8: Effect analysis of the Spatial Dynamic Panel Lag IV Fixed-Effects Model. Table 9 suggests that most interaction (cross-) terms exhibit a nonlinear relationship with energy consumption per capita. The _p_-values for all cross-terms are significantly below 0.01, indicating a strong association between the influential factors and energy consumption per capita. In Figure 10, panel (a) shows that when both GPP per capita (_GPPpc_) and land surface temperature at night (_Landtemp_night_) are high, energy consumption per capita is also high. Panel (b) illustrates that provinces with high _GPPpc_ and high _Rainfall_ tend to have higher energy consumption per capita. Panel (c) demonstrates that when _GPPpc_ and wind speed (_Windspeed_) are high, energy consumption per capita is also high. Similarly, panel (d) shows that provinces with high _GPPpc_ and high road density (_Roaddens_) tend to have higher energy consumption per capita. Areas with good wind circulation, well-connected roads, and easy access are more likely to attract human settlement and economic activity, which leads to increased energy use [57; 59; 61]. This pattern is consistent with the relationship observed with _Rainfall_. Panel (e) indicates that provinces with high land surface temperature at night (_Landtemp_night_) but low wind speed (_Windspeed_) tend to have high energy consumption per capita. This could be due to poor air circulation and elevated temperatures, which lead to greater use of air conditioners and energy consumption. Such conditions are often found in large urban areas with high levels of economic activity. Finally, panel (f) shows that provinces with both high land surface temperature at night (_Landtemp_night_) and high road density (_Roaddens_) also exhibit high energy consumption per capita. This may reflect highly urbanized areas having increased infrastructure and population density, leading to elevated energy usage. In conclusion, provinces with high GPP per capita (_GPPpc_), land surface temperature at night (_Landtemp_night_), rainfall (_Rainfall_), wind speed (_Windspeed_), and road density (_Roaddens_) tend to exhibit higher energy consumption per capita.