## 5 Results and Analysis
### Spatial Heterogeneity of Built Environment Factors Under the MGWR Model  
Through the analysis of the multicollinearity test, variables with a Pearson correlation coefficient greater than 0.8 were removed. Utilising the SPSSAU online software, a collinearity analysis among the independent variables was conducted [31]. The thickness of the lines in the diagram, as shown in Figure 3, represents the degree of correlation between the independent variables. Ultimately, eight independent variables were identified: road network density, population, accessibility, bus lines, bus stops, land use mix, office types, and residential types. These variables were analysed to examine the spatial heterogeneity influencing ridership into and out of rail transit stations. Before conducting the MGWR model analysis, a spatial autocorrelation test was performed on the built environment factors surrounding each rail transit station. The results of the spatial autocorrelation test, presented in Table 7, indicate that each built environment variable exhibits significant positive spatial correlation. The MGWR model was then employed to explore whether the impact of various types of built environments on ridership exhibits spatial heterogeneity. Prior to the calculation, the independent variables underwent standardisation. The results of this standardisation process are shown in Table 7.  
Using weekday peak hour ridership at each station (both entering and exiting) as the dependent variable, and road network density, population, accessibility, bus lines, bus stops, land use mix, office types, and residential types as independent variables, we substituted these into the MGWR model. The fitted coefficients for urban rail transit ridership (both entering and exiting stations) were obtained, as shown in Table 8. The statistics presented in the table include the mean, standard deviation (STD), minimum (Min), maximum (Max), bandwidth (BD), and \(p\)-value. The fitted coefficients can explain the degree of influence each independent variable has on the dependent variable. A positive coefficient indicates that the built environment factor positively promotes ridership at the station, with a larger absolute value indicating a greater degree of influence. Conversely, a negative coefficient indicates that the built environment factor hinders ridership, with a larger absolute value also indicating a greater degree of influence. The bandwidth reflects the spatial heterogeneity of the influence of the independent variables on the dependent \begin{table}
\begin{tabular}{c c c c c c} \hline
**NO.** & **Independent Variable** & **Mean** & **Min** & **Max** & **STD** \\ \hline
4 & Scenic spots & 25 & 0 & 186 & 11 \\
5 & Public services & 1020 & 0 & 9574 & 788 \\
6 & Office types & 594 & 4 & 4412 & 473 \\
7 & Residential types & 290 & 3 & 3008 & 196 \\
8 & Transportation hub & 237 & 14 & 2293 & 201 \\
9 & floor area ratio (FAR) & 0.82 & 0.03 & 4.68 & 1.75 \\
10 & Land use mix & 0.066 & 0.523 & 0.926 & 0.771 \\
11 & Road network density & 7.124 & 0.494 & 43.810 & 18.302 \\  & Number of entrances & & & & \\
12 & and exits of rail & 2 & 1 & 17 & 5 \\  & transit stations & & & & \\
13 & Accessibility & 12.37 & 23.44 & 83.78 & 34.15 \\
14 & Bus lines & 4 & 0 & 26 & 3 \\
15 & Bus stops & 4 & 1 & 27 & 9 \\ \hline \end{tabular}
\end{table} 
Table 6: _Cont._variable. A smaller bandwidth suggests a localised impact of the independent variable on the dependent variable, while a larger bandwidth indicates a global impact.