## 4 Results
### Spatial Patterns of Life Expectancy of Chinese Cities  
As can be seen from Table 2 and Figure 2, the average life expectancy of Chinese cities in 2000 was 72.01; the standard deviation was 3.07, and the coefficient of variation was 0.043. The maximum value was 79.19, which was in Shenzhen of Guangdong, and the \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Factors** & **Variables** & **Mean** & **Std. Dev.** & **Min** & **Max** \\ \hline \multicolumn{8}{c}{Dependent Variables} \\ \hline \multicolumn{8}{c}{Change in life expectancy} \\ \hline \multicolumn{8}{c}{Independent Variables} \\ \hline \multicolumn{8}{c}{Independent Variables} \\ \hline \multicolumn{8}{c}{Change rate of per capita GDP (base year 2000)} \\ \hline \multicolumn{8}{c}{Change in health care} \\ \hline \multicolumn{8}{c}{Independent Variables} \\ \hline \multicolumn{8}{c}{Change rate of per capita GDP (base year 2000)} \\ \hline \multicolumn{8}{c}{Change in health care} \\ \hline \multicolumn{8}{c}{Change rate of road density} \\ \hline \multicolumn{8}{c}{Change in average years of education} \\ \multicolumn{8}{c}{Change in aging rate} \\ \multicolumn{8}{c}{Change in structure} \\ \multicolumn{8}{c}{Change in birth rate} \\ \multicolumn{8}{c}{Change in gender ratio} \\ \multicolumn{8}{c}{Change in family size} \\ \hline \multicolumn{8}{c}{Average level} \\ \multicolumn{8}{c}{of air quality for many years} \\ \multicolumn{8}{c}{} \\ \multicolumn{8}{c}{} \\ \multicolumn{8}{c}{} \\ \multicolumn{8}{c}{} \\ Natural environment & \multicolumn{8}{c}{Average altitude (ln)} \\ \multicolumn{8}{c}{Average slope} \\ \multicolumn{8}{c}{} \\ \multicolumn{8}{c}{} \\ \multicolumn{8}{c}{} \\ \multicolumn{8}{c}{} \\ \multicolumn{8}{c}{} \\ \multicolumn{8}{c}{} \\ \multicolumn{8}{c}{} \\ \multicolumn{8}{c}{} \\ \multicolumn{8}{c}{} \\ \multicolumn{8}{c}{} \\ \end{tabular}
\end{table} 
Table 1: Definitions and descriptive statistics of variables. minimum value was 60.18, which was in Nujiang Lisu Autonomous Prefecture of Yunnan, with a difference of 19.01 years from the maximum. Compared with 2000, the average life expectancy of cities in 2010 increased to 76.37; the standard deviation was 2.30 and the coefficient of variation was 0.030. The maximum value increased to 83.52, which was in Xining of Qinghai, and the minimum value decreased to 63.76, which was in Nagqu of Tibet, with a difference of 19.76 years. Moreover, in 2000, the Moran's I index of life expectancy of cities in China was 0.581, dropping to 0.453 in 2010, and the Moran's I index of the change in life expectancy was 0.281 (Table 2). The coefficient of variation is lower than that in 2000, which means that the gap in life expectancy of Chinese cities shows a narrowing trend. The growth rate of life expectancy in areas with higher life expectancy is lower than that in areas with lower life expectancy, that is, the initial level of life expectancy is negatively correlated with the increase in life expectancy (preliminary verification of convergence). Compared with 2000, Moran's I index of life expectancy of cities in 2010 is decreased, but both are positive, indicating that although life expectancy of cities in 2000 and 2010 shows an obvious spatial agglomeration trend, the agglomeration in 2010 is lower than that in 2000, and the decentralization trend is relatively enhanced. The Moran's I index of the change in life expectancy is also positive. Thus, a universal explanation model is not enough to interpret the spatially heterogenous pattern of change in life expectancy. The GWR model provides a reasonable method for solving this problem. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Year** & **Min** & **Max** & **Std. Dev.** & **Mean** & **C.V.** \\ \hline
2000 & 60.18 & 79.19 & 3.07 & 72.01 & 0.043 \\
2010 & 63.76 & 83.52 & 2.30 & 76.37 & 0.030 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The gap in life expectancy of Chinese cities from 2000 to 2010.