## 4 Analysis
### GWR Results  
Here, we explore the spatially varying relationships between the dependent variable and potential influencing variables with GWR with the two sets of crop-water modeling data for the 1990s and the 2000s. In the OLS analysis, we found that crop yield deviation had a relatively strong correlation with population redistribution, whereas there was no obvious correlation between any of the other three environmental change factors and population redistribution. In the GWR analysis, we investigated the spatial correlation between crop yield deviation and population redistribution. The white part of Figures 3 and 4 shows the area without data, and the gray part represents areas that did not exhibit significant correlations (\(t\)-values with significance less than 90%). The green areas represent areas with positive spatial correlations, and the red areas represent those with negative spatial correlations. The results show that MeanYield was positively correlated with population redistribution in most areas. Figure 3: Spatial distribution of correlation coefficients of MeanYield and population redistribution in Mexico. The first, second, and third rows show the distributions of the correlation coefficients under no control variable (Model 1), with Built-up as a control variable (Model 2), and Pop as a control variable (Model 3), respectively. The first and second columns present the coefficient distributions of MeanYield calculated using the LPJmL_Gswp3 and LPJmL_Princeton model data, respectively, for 1990–2000, and the third and fourth columns present the corresponding distributions for 2000–2010. Figure 4: Spatial distribution of correlation coefficients of MeanYield and population redistribution in Ethiopia. The first, second, and third rows show the distributions of the correlation coefficients under no control variable (Model 1), with Built-up as a control variable (Model 2), and Pop as a control variable (Model 3), respectively. The first and second columns present the coefficient distributions of MeanYield calculated using the LPJmL_Gswp3 and LPJmL_Princeton model data, respectively, for 1990–2000, and the third and fourth columns present the corresponding distributions for 2000–2010. Figure 3 shows the spatial distribution of the correlation coefficients between crop yield deviation and population redistribution in Mexico. The first, second, and third rows show the distributions of the correlation coefficients of MeanYield with no control variable (Model 1), Built-up as a control variable (Model 2), and Pop as a control variable (Model 3), respectively. The first and second columns present the coefficient distributions of MeanYield calculated using the LPJmL_Gswp3 and LPJmL_Princeton model data, respectively, for 1990-2000, and the third and fourth columns present the corresponding distributions for 2000-2010. Figure 4 shows the spatial distribution of the coefficients of the correlation between crop yield deviation and population redistribution in Ethiopia, which is consistent with Figure 3.  
In Mexico, with no control variable (Model 1), the correlation between MeanYield and population redistribution was positive; positive coefficients were mainly distributed in the capital and nearby areas and gradually decreased from the capital to the surrounding areas. For 1990-2000, only parts of the west coast showed negative correlations (Figure 3, top row of panels). When including Built-up as a control variable (Model 2), the distribution of correlation coefficients was similar to that for Model 1; however, under Model 2, the positive coefficient areas were more concentrated in the densely populated capital city and nearby areas, and there were almost no areas with negative correlation coefficients. Therefore, the influence of crop yield deviation on population redistribution was more apparent when Built-up was controlled for. When population was included as the control variable (Model 3), we obtained results similar to those obtained with Model 1, with positive coefficients.