## 5 Analysis of Influencing Factors of Urban Vitality
### Exploration of the Spatial Relationship Between Urban Vitality and Influencing Factors
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Title 1** & **Subdistrict Level** & \multicolumn{2}{c}{**Block Level**} \\ \hline  & **OLS** & **MGWR** & **OLS** & **MGWR** \\ \hline R\({}^{2}\) & 0.913 & 0.933 & 0.707 & 0.824 \\ R\({}^{2}\) adjusted & 0.896 & 0.923 & 0.702 & 0.804 \\ AICc & 45.297 & 31.723 & 1331.317 & 1081.958 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Model diagnostic coefficients. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Variable** & **Max** & **Median** & **Min** & **Average** & **Standard Deviation** \\ \hline Resident population density & 0.413 & 0.208 & \(-\)0.075 & 0.210 & 0.162 \\ Building height & 0.318 & 0.315 & 0.303 & 0.314 & 0.003 \\ Commercial facility & 0.415 & 0.411 & 0.407 & 0.411 & 0.002 \\ accessibility & & & & & \\ Cultural and leisure facility accessibility & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Descriptive statistics of MGWR regression coefficients for the urban vitality at the subdistrict scale. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variable** & **Max** & **Median** & **Min** & **Average** & **Standard Deviation** \\ \hline Resident population density & \(-\)0.058 & \(-\)0.060 & \(-\)0.070 & \(-\)0.061 & 0.004 \\ Building height & 0.247 & 0.132 & 0.01132 & 0.123 & 0.066 \\ Greening rate & 0.020 & \(-\)0.100 & \(-\)0.239 & \(-\)0.089 & 0.084 \\ Functional mixing degree & 0.098 & 0.091 & 0.074 & 0.089 & 0.007 \\ Metro accessibility & 0.145 & \(-\)0.379 & \(-\)1.870 & \(-\)0.545 & 0.530 \\ Road network density & 0.240 & 0.136 & \(-\)0.047 & 0.131 & 0.072 \\ Commercial facility & 0.347 & 0.198 & 0.015 & 0.174 & 0.103 \\ accessibility & & & & & \\ Public facility accessibility & 0.120 & 0.113 & 0.100 & 0.111 & 0.006 \\ Cultural and leisure & 0.647 & 0.102 & \(-\)0.156 & 0.155 & 0.164 \\ facility accessibility & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Descriptive statistics of MGWR regression coefficients for the urban vitality at the block scale. In terms of correlation strength, the MGWR model results are consistent with those obtained using the optimal parameter geographic detector method. At the subdistrict scale, the factors influencing comprehensive vitality, in descending order of impact, are commercial facilities accessibility, cultural and leisure facilities accessibility, building height and resident population density. At the block scale, the order of influence is metro accessibility, commercial facilities accessibility, cultural and leisure facilities accessibility, road network density, building height, public facilities accessibility, functional mixing degree, greening rate and resident population density. Commercial facilities accessibility and cultural and leisure facilities accessibility exert the greatest influence on comprehensive vitality at both the subdistrict and block scales, whereas resident population density and building height exhibit comparatively weaker effects. According to the standard deviation index, resident population density shows substantial spatial variation in its influence on subdistrict vitality, while the variability associated with commercial facilities accessibility and cultural and leisure facilities accessibility is minimal. For block vitality, metro accessibility demonstrates considerable spatial variability in its influence, whereas resident population density, public facilities accessibility and functional mixing degree display limited variability. The model outputs were visualized and examined using ArcGIS10.81 (Figures 9 and 10). At the macro level, four variables, namely the resident population density, building height, commercial facilities accessibility and cultural and leisure facilities accessibility, have a significant influence on the formation of urban vitality. With the exception of the resident population density, the other three variables exhibit a positive correlation with the urban vitality index at the subdistrict level.