## 3 Results  
### Results of MLR Models and Evaluation of Multi-Scale BCEs  
#### 3.1.1 Results of MLR between BCE and Remote Sensing Data  
Tables 2 and 3 show the multiple linear regression results for BCEs from public and residential buildings by remote sensing data, respectively. Table 1 shows that the population (POP), public built-up land (PLU), summer temperature (ST), and winter temperature (WT) results are effective. These factors positively affect public BCEs, indicating that the large population size, high proportion of public built-up land, and high temperatures in summer and winter cause higher levels of CO\({}_{2}\) to be produced in public building operations, which is consistent with the trend of higher energy demand in urban areas where socio-economic activities are concentrated. The NCRJ results showed that the nighttime light, population size, public built-up land, and summer temperature were effective. The BCEs of prefectures in the NCRJ have seen a downward trend in recent years, and increased factors, such as nighttime light and public built-up land, have adversely affected public BCEs. Table 3 shows the regression results between residential BCEs and remote sensing data. The nighttime light and population size positively affect residential BCEs in the BTH. The NCRJ's regression results showed that the nighttime light, population size, enhanced vegetation index (EVI), and summer temperature positively affect residential BCEs. In particular, the population size and summer temperature positively affect the residential BCEs, whereas nighttime light and enhanced vegetation index negatively affect residential BCEs. On the one hand, they have been affected by reduced emissions from residential buildings since 2015. On the other hand, due to a lower population density and social and economic activities, areas with a higher degree of vegetation consume relatively less energy. Although the significant effect of vegetation cover on surface temperature and urban heat island which affecting buildings' energy consumption indirectly are proposed from previous studies [38; 39], the regression results of EVI did not show a significant impact on BCEs, especially in BTH urban agglomeration. We make a liner regression between EVI and BCEs (Figure A1). It can be found that results in BTH does not show significant correlation with BCEs but results in NCRJ show a relatively clear downtrend with EVI increasing, which is basically consistent with MLR models. In general, the results improved compared with the BCEs and NTL models (Tables A2 and A3). To further explain the fitting results of study areas, we compared the prefecture-level estimation results with prefecture-level statistical BCEs. Figures A2 and A3 show the comparison between the BTH and NCRJ, respectively. Figure A2a,c are the fitting results between estimation results using MLR and statistical results, showing almost consistent explanations for the estimations of public and residential BCEs with R\({}^{2}\), which are 0.76 and 0.82, respectively. Compared with the fitting results between estimation results using nighttime light data and statistical results (Figure A2b,d), estimation results using MLR are approaching the statistical results. Fitting results between prefecture-level estimation results and statistical results in the NCRJ also show consistency with Table 2, indicating the high explanation of statistical results to estimation results of public and residential BCEs with R2, which are 0.97 and 0.99, respectively (Figure A3). Table 4 lists the models for downscaling prefectures' BCEP and BCER to a grid scale in the BTH and NCRJ based on Equations (6) and (7).