## 3 Data and Methodology
### Methodology  
#### 3.3.1 Variable Selection  
Linear Correlation  
Initially, 26 candidate variables were selected to explore the factors influencing ride-hailing service demand (Table 1). An important preprocessing step before model building was to remove variables that were highly linearly correlated with others to avoid overfitting. To achieve this, we employed bidirectional stepwise regression, which balances model explanation and complexity by combining forward selection and backward elimination strategies [96]. In this method, forward selection tests the significance of each unselected variable and adds those that meet the significance threshold, while backward elimination re-evaluates the significance of variables already in the model and removes those that no longer meet the criteria. By dynamically adjusting the variable set at each step, this method selects key variables from the 26 candidates, ensuring that the final model includes only the statistically significant variables. Additionally, Variance Inflation Factor (\(VIF\)) analysis was performed to reduce the effects of multicollinearity. Multicollinearity occurs when independent variables are strongly correlated with one another, potentially distorting the interpretation of other variables' significance. The \(VIF\) is used to measure the severity of multicollinearity, with higher values indicating stronger correlations with other variables. The formula for \(VIF\) is calculated as in Equation (2):  
\[VIF_{k}=\frac{1}{1-R_{k}^{2}} \tag{2}\]  
where \(R_{k}^{2}\) is the regression coefficient of variable \(k\) on the remaining variables. The larger value of \(VIF_{i}\) indicates the higher degree of correlation between variable \(i\) and the other variables. According to existing research, a \(VIF\) value greater than 10 indicates significant multicollinearity, while a value below 5 suggests minimal concerns and is considered within a safe threshold. Spatial Autocorrelation  
In addition to linear correlation checks, another key issue in variable selection is the consideration of spatial autocorrelation, which is often overlooked in global models. Due to differences in spatial distribution of various functional zones within a city, human activities tend to exhibit significant spatial autocorrelation, meaning activity patterns in neighboring areas may show similarity or clustering effects. To assess spatial autocorrelation, this study applies global [PERSON]'s \(I\) index. As a widely used method for detecting spatial autocorrelation, it helps to identify spatial dependencies and clustering phenomena across the study area. The formula for [PERSON]'s \(I\) is calculated as follows in Equation (3):  
\[I_{k}=\frac{G}{\sum_{m=1}^{G}\sum_{n=1}^{G}w_{k}^{m,n}}\;\frac{\sum_{m=1}^{G} \sum_{n=1}^{G}w_{k}^{m,n}\left(x_{k}^{m}-\bar{x_{k}}\right)\left(x_{k}^{n}- \bar{x_{k}}\right)}{\sum_{m=1}^{G}\left(x_{k}^{m}-\bar{x_{k}}\right)^{2}},\; (m\
eq n) \tag{3}\]  
where \(I_{k}\) is the [PERSON]'s \(I\) index of variable \(k\), and \(x_{k}^{m}\) and \(x_{k}^{m}\) are the values of variable \(k\) at grid \(m\) and \(n\); there are a total of \(G\) grids; \(\bar{x_{k}}\) is the mean value of variable \(k\) at all grids, \(w_{k}^{m,n}\) is the spatial weight between grids \(m\) and \(n\), and \(I\) takes the value between \([-1,1]\). Higher positive [PERSON]'s \(I\) index values mean that close observations tend to have similar attribute values, while distant observations have different attribute values, which indicates spatial aggregation. However, a negative index indicates spatial dispersion, while an index near zero indicates a spatially random distribution. The null hypothesis of [PERSON]'s \(I\) is that the variable is randomly distributed without spatial correlation; i.e., \(I=0\)The \(Z\)-score is usually adopted as the significance index of the Moran index test, as shown in Equation (4):  
\[Z(I)=\frac{I-E(I)}{\sqrt{Var(I)}} \tag{4}\]  
where \(E(I)\) and \(Var(I)\) are the expectation and the standard deviation of the [PERSON]'s \(I\) statistic, respectively.