## 5 Results and Discussion
### Model Implementation and Results Analysis  
Strong spatial autocorrelation is found for all of the variables included in our study. Thus, it is feasible to implement GWR models to explore the association between Shenzhen Metro ridership and its influencing factors. The final selection of explanatory variables derived from the backward stepwise regression method for the five models is given in Table 4.  
Table 4 enables us to find the common explanatory variables among the five models and the individual variables of each model. The common explanatory variables are the major factors impacting metro ridership, including population, betweenness centrality, and days since opening. The different individual variables of the five models indicate that factors affecting station-level ridership differ by the day of the week and time of the day. The number of offices within the PCA and the distance from the station to the city center are individual variables in the model for average weekday ridership. The number of residences and shopping places within the station catchment area is related to the average weekend ridership. Thus, commuting activities appear to mainly affect the average weekday ridership, while recreational activities related to commercial development such as shopping malls mainly affect the average weekend ridership. Across a single day, the number of schools and the distance to the center mainly affect the evening rush hour ridership, while the number of shopping places and the distance to the center mainly affect the nonrush hour ridership. Thus, passengers from schools (primary schools, high schools, and universities) contribute to the evening rush ridership and noncommuting activities like shopping affect the nonrush hour ridership. Due to limitations on space, we only compare the results of Model 5 with those of the OLS model in Table 5, and we give the results of Models 1-4 compared with those of the OLS models in Appendix A (Tables A1-A4). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Variables** & **Model 1** & **Model 2** & **Model 3** & **Model 4** & **Model 5** \\ \hline \
\begin{tabular}{c} **Response** \\ **Variable** \\ **(Ridership)** \\ \end{tabular} & Weekly\_ridership & Weekday\_ridership & Weekend\_ridership & Weekend\_ridership & Eventush\_ridership & Nonrush\_ridership \\ \hline \multirow{4}{*}{
\begin{tabular}{c} **Explanatory** \\ **Variables** \\ **Variables** \\ \end{tabular} } & Pop & Pop & Pop & Pop & Pop \\ \cline{1-1}  & Betweenness & Betweenness & Degree & Degree & Degree \\ \cline{1-1}  & Days\_open & Days\_open & Betweenness & Betweenness & Betweenness \\ \cline{1-1}  & Shopping & Office & Days\_open & Days\_open & Days\_open \\ \cline{1-1}  & Dis\_to\_center & Dis\_to\_center & Residence & School & Shopping \\ \cline{1-1}  & & Shopping & Dis\_to\_center & Dis\_to\_center \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Variables selected in the models. First, Table 5 shows that the AICc values of all of the GWR models are smaller than those of the corresponding global regression (OLS) models. According to the evaluation criterion proposed by [PERSON] et al. (1996) [19], if the difference between the AICc values of a GWR model and an OLS model is more than 3, the GWR model can be considered more applicable than the OLS model, even though it is more complex. The adjusted R-squared values of the GWR models are greater than those of the corresponding OLS models, demonstrating that the GWR model has strong explanatory power even when considering model complexity. Likewise, the parameter values (Sigma) indicating the model error of the GWR models are lower, and the residual sum of the squares from the GWR models are smaller than those from the OLS models. Thus, the results show that the GWR models generally perform better in goodness-of-fit measures than the OLS models. ANOVA tests, as shown in Table 5, are conducted to find out if the global (OLS) regression model and the GWR model have the same statistical performance (the same size of error variance).