## 3 Results and Analysis
### The Impact Path Test of Urbanization on Carbon Emissions
The partial regression coefficient of the urbanization level (\(lnU\)) for economic development (\(lnG\)) is 0.959 and it is statistically significant at the 5% significance level (Column8), indicating that an improvement in the urbanization level will promote economic development. (3) The mediating effect test. \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Urbanization (\(lnU\))\(\rightarrow\)The Proportion of Secondary Industry**} & \multicolumn{3}{c}{**Urbanization (\(lnU\))\(\rightarrow\)The Proportion of tertiary Industry**} & \multicolumn{3}{c}{**Urbanization (\(lnU\))\(\rightarrow\) Economic Development Level**} \\  & \multicolumn{3}{c}{**(\(lnC_{1}\))\(\rightarrow\)Carbon Emission (\(lnY\))**} & \multicolumn{3}{c}{**(\(lnC_{2}\))\(\rightarrow\)Carbon Emission (\(lnY\))**} & \multicolumn{3}{c}{**(\(lnG\))\(\rightarrow\)Carbon Emission (\(lnY\))**} \\ \cline{2-10}  & \multicolumn{1}{c}{_InvT(total)_} & \multicolumn{1}{c}{\(LnC_{1}\)} & \multicolumn{1}{c}{\(lnY\)} & \multicolumn{1}{c}{\(lnY\)(total)} & \multicolumn{1}{c}{\(lnC_{2}\)} & \multicolumn{1}{c}{\(lnY\)} & \multicolumn{1}{c}{\(lnY\)(total)} & \multicolumn{1}{c}{\(lnG\)} & \multicolumn{1}{c}{\(lnY\)} \\ \cline{2-10}  & \multicolumn{1}{c}{_Column1_} & \multicolumn{1}{c}{_Column2_} & \multicolumn{1}{c}{_Column3_} & \multicolumn{1}{c}{_Column4_} & \multicolumn{1}{c}{_Column5_} & \multicolumn{1}{c}{_Column6_} & \multicolumn{1}{c}{_Column7_} & \multicolumn{1}{c}{_Column8_} & \multicolumn{1}{c}{_Column9_} \\ \hline lnG & 0.085 & 0.072 & 0.071 & 0.085 & 0.208 & 0.087 & & & 0.085 \\  & [0] *** & [0] *** & [0] *** & [0.545] & [0] *** & & & [0] *** \\ InP & 0.820 & 0.793 & 0.820 & & 0.786 & 0.881 & & 0.820 \\  & [0] *** & & [0] *** & [0] *** & & [0] *** & & [0] *** \\  & 0.828 & 0.805 & 0.828 & & 0.819 & 0.757 & & 0.828 \\  & [0] *** & & [0] *** & [0] *** & & [0] *** & & [0] *** \\  & [0] *** & & [0] *** & [0] *** & & [0] *** & [0] *** & & [0] *** \\ InU & 0.044 & 0.035 & 0.071 & 0.044 & 0.028 & 0.056 & 0.167 & 0.959 & 0.044 \\  & [0.014] * & [0.001] *** & [0] *** & [0.014] * & [0.014] * & [0.002] * & [0] *** & [0.014] * & [0.014] *** \\  & & 0.175 & & & & 0.013 & & & \\  & & & [0] *** & & & [0.038] * & & & \\ W\({}^{\rm{th}}\)Y & 0.413 & & 0.641 & 0.413 & & 0.363 & 0.623 & & 0.413 \\  & [0] *** & & [0] *** & [0] *** & & [0] *** & [0] *** & & [0] *** \\ W\({}^{\rm{th}}\)G & 0.175 & 0.188 & & 0.119 & 0.012 & & 0.063 & 0.012 \\  & & [0] *** & [0.031] * & [0] *** & [0] *** & [0.452] & & [0] *** & [0.452] \\ W\({}^{\rm{th}}\)P & & & 0.002 & & & 0.002 & \(-\)0.456 & & 0.002 \\  & & [0.991] & & & [0.991] & [0] * & & [0.991] \\ W\({}^{\rm{th}}\)T & & & \(-\)0.105 & & & \(-\)0.105 & \(-\)0.323 & & \(-\)0.105 \\  & & [0.013] * & & & [0.013] * & [0] *** & & [0.013] * \\ W\({}^{\rm{th}}\)U & \(-\)0.088 & \(-\)0.025 & 0.113 & \(-\)0.088 & 0.048 & \(-\)0.129 & 0.123 & 0.048 & \(-\)0.088 \\  & [0.079] * & [0.536] & [0.004] *** & [0.079] * & [0.169] & [0.006] *** & [0] *** & [0.169] & [0.079] * \\  & & 0.175 & \(-\)0.188 & & 0.125 & 0.308 & & & \\  & & [0] *** & [0.031] * & [0.021] * & [0.007] *** & & & & \\ R\({}^{2}\) & 99.66\% & 87.85\% & 99.67\% & 99.66\% & 94.58\% & 99.61\% & 99.57\% & 94.58\% & 99.66\% \\ \hline \hline \end{tabular} Note: Inside of the [ ] is the \(p\)-value; *, **, and *** indicate statistically significant differences at the 10%, 5%, and 1% levels, respectively.  
\end{table} 
Table 6: Impact path test result of Urbanization \(\rightarrow\) Mediating Variables \(\rightarrow\) Carbon Emissions. The estimation results of Column1 to Column9 in Table 6 show that the coefficients of \(lnU\) are statistically significant at the significance level of 5%, indicating that \(lnC_{1}\), \(lnC_{2}\), and \(lnG\) are significant mediator variables, and all of them are partial mediating effects. The explanation for this is that there is a pathway through which urbanization significantly affects carbon emissions by affecting the level of economic development and the proportion of secondary and tertiary industries.