## 3 Results
Thus, the MGWR analysis shows a strong, spatially varying relationship between food deserts and cardiovascular health patient rates in Greater Santiago. The enhanced explanatory power and improved model fit highlight the critical need for spatially explicit approaches in public health research enabling more targeted and effective interventions. Figure 4 illustrates the local \(r^{2}\) values of the MGWR model applied to Greater Santiago. The map is divided into Census Zones, each shaded according to their local \(r^{2}\) values, which indicate the proportion of variance in the rate of elderly cardiovascular health patients explained by the probability of food deserts within each zone. The color gradient ranges from light grey to dark blue, representing increasing values. The lightest shade \begin{table}
\begin{tabular}{l c c} \hline \hline
**Variable** & **Intercept** & **Food Desert Probability** \\ \hline Mean & 0.037 & 0.162 \\ \hline Standard Deviation (STD) & 0.378 & 0.554 \\ \hline Minimum & \(-\)0.354 & \(-\)0.709 \\ \hline Median & \(-\)0.063 & 0.055 \\ \hline Maximum & 2.623 & 5.051 \\ \hline Bandwidth & 59.000 & 47.000 \\ \hline Effective Number of Parameters (ENP\_j) & 65.682 & 93.718 \\ \hline Adjusted t-value (95\%) & 3.373 & 3.470 \\ \hline Degrees of Dependence (DoD\_j) & 0.434 & 0.386 \\ \hline Bandwidth Confidence Intervals (95\%) & (50 63) & (45 47) \\ \hline Diagnostic information: Residual sum of squares: 778.466; Log-likelihood: \(-\)1705.619; Corrected Aikaike Information Criterion (AICc): 3767.512; \(r^{2}\): 0.520; adjusted \(r^{2}\): 0.467. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: MGWR results. (light grey) corresponds to the lowest local \(r^{2}\) values, indicating areas where the MGWR model explains a minimal portion of the variance. These zones include parts of central and northern Santiago, such as Conchali, Lo Prado, Estacion Central, Carrillos, and some areas of La Reina and Vitacura. The darkest blue areas represent the highest local \(r^{2}\) values, suggesting a strong explanatory power of the model in these regions. Notably, these high \(r^{2}\) zones are found in the southern and eastern parts of the city, such as San Bernardo, La Pintana, Puente Alto, and Lo Barnechea, mostly related to low-income communities. Nevertheless, the \(r^{2}\) is also high in wealthier areas such as Vitacura, Nunoa, and Las Condes. On the other hand, the \(r^{2}\) shows more heterogeneity in Providencia, Recoleta, and Santiago. Areas with higher \(r^{2}\) values likely face a more pronounced impact from food deserts on cardiovascular disease rates, pointing to critical zones for targeted public health interventions. Conversely, regions with lower values may require additional factors to be considered to fully understand the drivers of cardiovascular health disparities. Figure 5 presents the spatial distribution of residuals from the MGWR model for Greater Santiago. The residuals are color-coded, ranging from light pink (indicating negative residuals) to dark red (indicating positive residuals). Negative residuals suggest that the model overpredicted the rate of elderly cardiovascular health patients, while positive residuals indicate underpredictions. Figure 4: Local \(r^{2}\) of MGWR in Greater Santiago. Notably, central areas such as Santiago and Nunoa display mostly negative residuals, implying overestimation by the model. Conversely, southern zones such as La Pintana and Puente Alto exhibit positive residuals, suggesting underestimation. This spatial pattern highlights areas where the MGWR model's predictions are less accurate, indicating potential factors not captured by the model. The darker areas are where the model is more accurate, indicating that in relevant parts of the city the model works well. In all the municipal areas of the city there are at least two censal zones where the model offers small residuals, making it suitable to advance in a lower scale of analysis.