## 3 Results  
Initially, a global regression model was applied to investigate the relationship between food desert probability and the rate of elderly cardiovascular health patients (Table 1). The results of the global model indicate a very low r\({}^{2}\) value of 0.013, which suggests that the model explains only 1.3% of the variance in the dependent variable. Furthermore, the adjusted r\({}^{2}\) remains at 0.013, confirming the weak explanatory power of the model. The Akaike Information Criterion corrected for small samples (AICc) is 4584.193, which is relatively high and suggests poor model fit. The regression coefficient for food desert probability is estimated at 0.116 with a standard error of 0.025, resulting in a statistically significant t-value of 4.706 and a \(p\)-value of less than 0.001. This indicates a positive association between food desert probability and the rate of elderly patients in the cardiovascular program, albeit with limited predictive power. In contrast, the MGWR model, which allows for spatially varying relationships, provides a significantly improved fit. The MGWR model achieves an r\({}^{2}\) value of 0.520, indicat \begin{table}
\begin{tabular}{l c c} \hline \hline
**Variables:** & **Intercept** & **Food Desert Probability** \\ \hline Estimated values & 0.000 & 0.116 \\ \hline Standard Error & 0.025 & 0.025 \\ \hline \(t\)-statistic & 0.000 & 4.706 \\ \hline \(p\)-value & 1.000 & 0.000 \\ \hline \hline \end{tabular} Diagnostic information: Residual sum of squares 1599.128; Log-likelihood: \(-\)2289.089; AICc: 4584.193; r\({}^{2}\): 0.013; adjusted r\({}^{2}\): 0.013.  
\end{table} 
Table 1: Global regression results. ing that it explains 52.0% of the variance in the rate of elderly cardiovascular health patients. The adjusted \(r^{2}\) is slightly lower at 0.467, but still represents a substantial improvement over the global regression model. The Corrected Aikaike Information Criterion (AICc) for the MGWR model is 3767.512, a marked reduction from the global model, highlighting the superior ability of MGWR to capture spatial variations in the data (Table 2). The MGWR model utilizes an adaptive bisquare kernel to determine spatial weights and employs the golden section search method for optimizing bandwidth selection. The results show that the bandwidth for the intercept is 59, while the bandwidth for the food desert probability is 47, indicating that the spatial influence of these variables varies across the study area. The summary statistics for the MGWR parameter estimates revealed substantial spatial heterogeneity in the relationship between the variables. The mean estimate for the intercept was 0.037, with a standard deviation of 0.378 and a range from \(-\)0.354 to 2.623. This variability suggests that the baseline rate of elderly cardiovascular health patients varies significantly across different Census Zones. The mean estimate for food desert probability is 0.162, with a standard deviation of 0.554 and a range from \(-\)0.709 to 5.051, indicating that the impact of food deserts on cardiovascular health patient rates was also spatially variable. The substantial increase in \(r^{2}\) from the global regression model to the MGWR model underscores the importance of accounting for spatial heterogeneity in the analysis. The MGWR model's ability to reveal localized variations provides a more nuanced understanding of the factors influencing cardiovascular health outcomes. Specifically, the spatial variability in the relationship between food desert probability and cardiovascular health patient rates suggests that interventions to address food deserts may need to be tailored to specific neighborhoods within Greater Santiago. The significantly lower AICc value for the MGWR model further confirms its superior fit and predictive capacity. This improvement suggests that the MGWR model more accurately captures the underlying spatial processes affecting cardiovascular health, thereby offering valuable insights for public health planning and policy development.