## 4 Results
### Prediction of Elderly Care Facility Locations  
This study employed a fine-grained grid scale to conduct quantitative simulations for the siting and layout of elderly care facilities. The Random Forest algorithm was utilized to predict 5839 potential suitable locations. The prediction results were subsequently imported into the ArcGIS platform for spatial visualization. The preliminary prediction results (Figure 9) reveal that the spatial distribution of existing elderly care facilities in Changsha City exhibits substantial clustering characteristics. These facilities are predominantly concentrated in central urban districts, including Yuhua District, Tianxin District, and Furong District, demonstrating a distinct decreasing gradient from the center to the periphery. Spatial pattern analysis indicates that the predicted suitable locations on the east bank of the Xiangjiang River substantially outnumber those on the west bank. Multiple concentrated distribution zones were identified in peripheral regions such as Liuyang City and Ningxiang City. Notably, while most existing facilities are located within predicted suitable grid cells, a substantial number of suitable grid cells remain underutilized. Particularly prominent clusters were observed in Dayao Town (Liuyang City), Huangcai Town (Ningxiang City), and Jinjing Town (Changsha County), which could be prioritized as key areas for future development of elderly care facilities. Figure 8: Spatial distributions of local coefficients (15 min life circle) and t-value with significantly <90%. Given that the preliminary selection of 5839 candidate locations substantially exceeds Changsha City's near-term planning requirements, this study developed a refined three-stage screening mechanism: First, based on data from the Seventh National Population Census, streets with a population aged 65 and above exceeding 13% were identified. These areas, where the elderly population proportion is substantially higher than the average level in Changsha City (13%), are deemed priority areas for construction. Second, considering the scale effect and service capacity of elderly care facilities, a second-level screening criterion was applied to select areas with an elderly population (aged 65 and above) exceeding 7000 people. This threshold aligns with the average elderly population size at the street level in Changsha City. Finally, within the streets meeting the above criteria, spatial overlay analysis was conducted to exclude areas where elderly care facilities have already been established. This ensures that new facilities can effectively fill service gaps and optimize the spatial distribution efficiency of elderly care facilities. This multi-tiered screening approach not only enhances the scientific rigor of site selection but also provides valuable reference for government decision-making in near-term construction planning.The final result is shown in Figure 10.  
Figure 10: Selected Site Selection. Figure 9: Preliminary Site Selection. Within the ring expressway of Changsha City, the aging phenomenon is pronounced, with a large number of streets. Although existing elderly care facilities are relatively concentrated, the number of predicted sites remains substantial. Further analysis of the built environment along inner-ring streets reveals that GWR results show a significant positive correlation between building density and walkability scores within a 10-min walking threshold. Therefore, prioritizing high-density areas for elderly care facility placement is advisable, as these zones typically offer better access to commercial, medical, and service infrastructure, enhancing convenience for older adults. To optimize planning, the model-predicted high-density zones could be overlaid with existing facility distributions to identify \"10-min walking coverage blind spots\", where compact elderly care service centers should be prioritized.