## 3 Results
### Model Result from OLS  
The correlation matrix of the explanatory variables is shown in Table 1. The selected variables show no significant correlation (\(\alpha\) = 0.01). All the coefficients (\(\beta\)) of the variables except for that of the grazing intensity show significance (\(p\) \(<\) 0.01), indicating that at the global scale, population density, road network density, and NPP all imposed a significant impact on RCU (Table 2). The positive coefficients from population and NPP reveal that a higher population density and NPP generally tend to contribute RCU or more loss in vegetation carbon sequestration. The negative coefficient from the road network density suggests that more road networks led to lower RCU or less carbon loss in carbon sequestration. Grazing intensity has for a long time been regarded as a factor affecting the grassland vegetation [41]. The positive coefficient (\(\beta\) = 0.65) of grazing intensity suggests that high grazing generally reduced carbon sequestration from vegetation; at the same time, the insignificance (\(p\) = 0.66) in the coefficient implies that the grazing might demonstrate local variation in the impact on vegetation productivity. The variance inflation factors (VIFs) all showed low value (\(<\)7.5), suggesting there is no problem of redundancy (multicollinearity) among the explanatory variables.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variable \#** & **Population** & **Road** & **NPP** & **Grazing** \\ \hline Population & 1.00 & & & \\ Road & 0.27 & 1.00 & & \\ NPP & 0.02 & \(-\)0.17 & 1.00 & \\ Grazing & \(-\)0.13 & \(-\)0.06 & \(-\)0.14 & 1.00 \\ \hline \hline \end{tabular} \# Population = population density; Road = road network density; Grazing = grazing intensity.  
\end{table}
Table 1: Correlation matrix between the explanatory variables.  
Figure 3: Distribution of reduced carbon uptake (RCU) at the pixel scale (with RCU\({}_{\text{mean}}\) = 58.9 \(\pm\) 2.3 gC m\({}^{-2}\) yr\({}^{-1}\)) and the aggregated administrative unit level. (**a**) Temporally averaged reduced carbon uptake (RCU) (2001–2018), and (**b**) Zonal average at the administrative-unit scale.  
The overall performance of the OLS model is summarized in Table 3. The Jarque-Bera statistic, which is a goodness-of-fit test of whether the data present skewness and kurtosis, shows non-significance (\(p\) = 0.56), indicating that the residuals from the OLS model are not significantly different from normal distribution. The Joint Wald statistic confirmed the model significance (\(p\)<0.01). However, a rather low percentage, i.e., 21% (adjusted R\({}^{2}\) = 0.21), of the variation in RCU is explained from the explanatory variables by the OLS model. The significance of the Koenker (BP) Statistic (\(p\) < 0.01) suggests that a local regression such as GWR may be a better model candidate.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Variable** & **Coef. (\(\beta\))** & **StdErr.** & **t-Statistics** & **Probability** & **Robust\_SE** & **Robust\_t** & **Robust\_Pr** & **VIF** \\ \hline Intercept & 51.49 & 43.80 & 1.17 & 0.24 & 45.80 & 1.12 & 0.27 & \\ Population & 0.35 & 0.13 & 2.62 & \textless{}0.01 \({}^{*}\) & 0.13 & 2.67 & \textless{}0.01 \({}^{*}\) & 4.87 \\ Road & \textless{}0.91 & 0.44 & \textless{}2.07 & 0.04 \({}^{*}\) & 0.51 & \textless{}1.79 & 0.08 & 4.82 \\ NPP & 0.30 & 0.08 & 3.95 & \textless{}0.01 \({}^{*}\) & 0.10 & 3.15 & \textless{}0.01 \({}^{*}\) & 1.04 \\ Grazing & 0.65 & 2.01 & 0.33 & 0.74 & 1.50 & 0.44 & 0.66 & 1.04 \\ \hline \hline \end{tabular} \({}^{*}\)Significance tested based on two-tailed hypothesis; VIF = variance inflation factor.  
\end{table}
Table 2: Statistics of the regression coefficient for the explanatory variables from ordinary least square (OLS) regression.  
Figure 4: Distribution of selected explanatory variables for the reduced carbon uptake (RCU) from vegetation. (**a**) Grazing intensity, (**b**) Population density, (**c**) Road network density, and (**d**) Net primary productivity (NPP) at the administrative unit level.