## 5 Results and Discussion
### Model Implementation and Results Analysis
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **OLS** & **GWR** \\ \hline Moran’s index & 0.108184155 & \(-\)0.114488799 \\ Expected index & \(-\)0.008547009 & \(-\)0.008547009 \\ Variance & 0.002855149 & 0.002870601 \\ z-score & 2.18460251 & \(-\)1.9773379 \\ \(p\)-value & 0.01446 & 0.976 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Global Moran’s I residuals test of the models for the average ridership across the whole week. Figure 4: Standardized residuals of GWR for average weekday ridership (Model 2). Figure 5: Local indicator of spatial association (LISA) cluster maps of residuals in the OLS and GWR models. Colors indicate significant positive (red and pink), negative (pale blue and yellow), and not significant (blue) spatial autocorrelation. (**a**) LISA cluster map of residuals of OLS model for the average ridership across the whole week. (**b**) LISA cluster map of residuals of GWR model for the average ridership across the whole week. out, implying that GWR makes a significant improvement over OLS in terms of model fitting from the perspective of residuals. Using the Voronoi algorithm [38], the Shenzhen Metro coverage area can be divided into several Thiessen polygons according to the locations of the stations. Here, the spatial distribution of the local R-squared and local coefficients is visualized using Thiessen polygons. The values of the local R-squared range between 0 and 1, which indicates the satisfactory fitting of the local regression model. Mapping the local R-squared values can help us to see where GWR has a higher predictive capacity and where it performs poorly. Figure 6 illustrates the spatial distribution of the local R-squared of Model 2 for average weekday ridership and Model 5 for nonrush hour ridership, enabling us to understand where the model has a stronger explanatory power (local R-squared). Both Model 2 and Model 5 have a higher explanatory power in the central-north and southeast regions than in the other regions. In addition, the local R-squared values of most of the stations are higher than 0.82; these stations are mainly located in Luohu district. By understanding the spatial distribution of local coefficients (elasticities) and \(t\)-values (significance), we can determine how the relationship between the variables changes spatially (estimated coefficients), and at what level of statistical significance. For example, in Model 2 (see Figure 7), as a common factor, the mean of the coefficients for the population variable is 3284.89. Thus, for each person within the station's PCA, the number of trips adds up to 3284.89 each weekday. However, these elasticities are distributed unevenly in space. More trips per capita are expected in the central zone and the mid-north, where commercial and administrative areas and educational institutions are intensively distributed, while elasticity values are lower in the west and east. The \(t\)-value map on the right also shows that the effect of population is more significant in the middle area at a 0.05 level (the absolute value of a \(t\)-value larger than 1.96) (Figure 7a). Figure 6: Spatial distribution of the local R-squared values of Model 2 and Model 5. (**a**) Local R-squared values’ distribution of Model 2 (average weekday). (**b**) Local R-squared values’ distribution of Model 5 (nonrush hour). For the individually selected factor in Model 2, the mean of the elasticities for the office variable is 2397.24. Thus, for each new office within the station's PCA, the number of trips adds up to 2397.24 each weekday. Elasticities are higher (more trips attracted per office) in the east and west than in the middle, whereas the elasticities of the central and north regions are negative and low, indicating that people who go to work in these regions depend more on transport other than the metro. In addition, the t-value map on the right shows that the effect of offices is more significant in the east, west, and mid-south areas at a 0.05 level (the absolute value is larger than 1.96) (Figure 7b).