## 5 Results and Discussion
### Quadratic Response Surface Regression Analysis of Intervention Policies
From the point of view of the coefficient alone, the coefficient of support (\(x_{2}\)) is larger. For PCP, FCP, and CPP, the interaction coefficient of residents' degree of understanding and support is significant. This indicates that residents' degree of understanding and support have a significant interaction effect on the degree of implementation of these three kinds of policies. As can be seen from the results of Table 7, the R2 of Model 2 is significantly improved compared with Model 1. The coefficients of the quadratic term and interaction term in Model 2 are significant, indicating that Model 2 has higher explanatory power. The response analysis was further carried out through the three-dimensional graph. Specifically, MATLAB2021a software is used to draw the three-dimensional diagram of the relationship between residents' degrees of understanding, support, and implementation of energy-saving policies. As shown in Figure 2, when the consistency of residents' understanding and support of energy-saving policy is high (the consistency is, \(x_{1}=x_{2}\)), residents' degree of implementation of the policy is also high, and hypothesis H3 is true. The knowledge-attitude-behavior model [55] points out that behavior is related to knowledge and belief. Residents' understanding of policies needs to be supported by relevant knowledge. Residents' support for policies is an individual attitude and belief, which can predict the implementation of compliance policies. However, residents' understanding of policies does not translate directly into their implementation. The promotion of energy-saving knowledge should be emphasized. To a certain extent, this indicates that the government should pay attention to the consistency of residents' understanding and support for energy-saving policies and give consideration to the far-reaching influence of propaganda policies on residents' long-term intervention in energy-saving behaviors. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Price Control Policy (PCP)**} & \multicolumn{2}{c}{**Fee Collection Policy (FCP)**} \\ \cline{2-5}  & \multicolumn{2}{c}{**Y**} & \multicolumn{2}{c}{**Y**} \\ \cline{2-5}  & **Model 1** & **Model 2** & **Model 1** & **Model 2** \\ \hline \(x_{1}\) & 0.104 *** & 0.128 *** & 0.097 *** & 0.100 *** \\ \(x_{2}\) & 0.328 *** & 0.333 *** & 0.320 *** & 0.352 *** \\ \(x_{1}^{2}\) & & 0.023 & & \(-\)0.028 \\ \(x_{2}^{2}\) & & 0.003 & & 0.025 \\ \(x_{1}x_{2}\) & & \(-\)0.075 *** & & 0.092 *** \\ R\({}^{2}\) & 0.206 & 0.215 & 0.149 & 0.161 \\ F & 163.353 & 69.564 & 110.452 & 49.065 \\ \hline \hline  & \multicolumn{2}{c}{**Economic Subsidy Policy (ESP)**} & \multicolumn{2}{c}{**Campaign Publicity Policy (CPP)**} \\ \cline{2-5}  & \multicolumn{2}{c}{**Y**} & \multicolumn{2}{c}{**Y**} \\ \cline{2-5}  & **Model 1** & **Model 2** & **Model 1** & **Model 2** \\ \hline \(x_{1}\) & 0.141 *** & 0.150 *** & 0.188 *** & 0.206 *** \\ \(x_{2}\) & 0.443 *** & 0.280 *** & 0.460 *** & 0.481 *** \\ \(x_{1}^{2}\) & & 0.070 *** & & \(-\)0.105 *** \\ \(x_{2}^{2}\) & & \(-\)0.186 *** & & 0.002 \\ \(x_{1}x_{2}\) & & 0.054 & & \(-\)0.037 \\ R\({}^{2}\) & 0.149 & 0.175 & 0.196 & 0.221 \\ F & 110.400 & 54.148 & 153.764 & 71.946 \\ \hline \hline \end{tabular} Note: *** \(p<0.001\); \(x_{1}\) indicates residents’ degrees of understanding of energy-saving policies; \(x_{2}\) indicates residents’ degrees of support for energy-saving policies; \(Y\) indicates residents’ degrees of implementation of energy-saving policies.  
\end{table} 
Table 7: Results of quadratic response surface regression analysis.