## 4 Impact Factors of Urban Ecological Resilience in the BTHUA Region  
To analyze the correlation between urban ecological resilience and its impact factors (Table 1), a multiple linear regression model is built. Impact factors are selected based on previous studies and data availability. In this study, we try to include both physical geographical and socio-economic factors. For biophysical factors, climate factors including temperature and precipitation play important roles in the formation of ecosystem structure and function. They directly impact the growth of vegetation and thus tend to impact ecological resilience. In the study region, the annual mean temperature is decreasing from the southeast to the northwest (Figure 3a), while precipitation is concentrated in east Hebei plain and south Hebei (Figure 3b). Vegetation coverage is also significantly affected by topography and correlated with elevation and slope. The topography of the study region is high in the northwest and low in the southeast, tilting from the northwest to the southeast (Figure 3c). The slope rises from the southeast to the Taihang Mountains and drops to the northwest after the Taihang Mountains (Figure 3d). Socio-economic factors, including population, GDP, carbon emission, and built-up land, mark the impact of human activities on the urban ecosystem. As an important approach to regional sustainable development, urban resilience is a coordinated and optimized combination form of multiple factors such as economy, population, land and market. Among them, the built-up area is the spatial carrier of regional resource convergence and diffusion, which influences urban resilience through multiple forms of resource combination. Reasonable population spatial pattern and economic development pattern are the main ways for cities to deal with natural disasters and urban diseases. In the study region, the selected socio-economic indicators all show the characteristics of clustering towards the urban center (Figure 3e-h). The multiple linear regression results show that from the biophysical side, ecological resilience in the BTHUA region decreases with the increase of temperature and precipitation, showing that ecosystems in the high temperature and heavy rainfall areas in this region are less stable. Resilience decreases by 0.0389 for every 10-degree Celsius increase in temperature, and by 0.0089 for every 1000 mm precipitation increase, and the results are significant with a P value less than 0.001 (Table 2). Elevation and slope determine the spatial distribution of vegetation types to a large extent, and the degree of ecological resilience increases with the increase of average elevation in the region, with a 0.0093 increase in ecological resilience for every 1000 m elevation increase. In addition, ecological resilience in the study region increases by 0.0303 with every 10-degree slope increase. The system resilience is significantly correlated with topography (with P values both less than 0.001). However, from the socio-economic side, urban ecological resilience is positively related to GDP and negative related to population and built-up land. For every extra 100 people per unit km\({}^{2}\) area, resilience decreases by 0.0187%, while when built-up land expands, resilience tends to decrease significantly. For every 1 million increases in GDP per unit km\({}^{2}\) area, resilience increases by 0.00187%. It shows that the level of economic development has a significant positive impact on urban resilience. This can be attributed to the high overall economic development level in the BTHUA region; resources could be allocated to technological (new technologies that increase resources efficiency and reduce pollution) and institutional (stringent environmental protection policies and enforcements) advancement, generating benign ecological and environmental effects.