# Promotion Effects of High-Speed Rail on Urban Development: Evidence from Three Lines in China
## 3 Results
### Analysis Considering Relevant Influencing Factors
#### 3.2.3 Different Performances of Cities of Varying Urban Scales  
City size is also an important factor affecting the impact of HSR. Since city size is a continuous variable, we can plot a two-dimensional scatter plot for all city samples and attempt linear regression to reveal the patterns in the \(D_{aR}\), \(D_{aE}\), \(D_{aG}\), and \(D_{aL}\) indicator values for cities of different sizes. The analysis results are shown in Figure 5.  
It can be seen that the impact of HSR on different dimensions varies across cities of different sizes. The promotion of population aggregation by HSR is more significant in larger cities. In terms of slope, the promotion effect on employment population aggregation is even more pronounced. Conversely, the promotion of economic growth and construction land expansion by HSR is more significant in smaller cities. The goodness-of-fit values range from 0.0125 to 0.1487, indicating that the fit of the linear regression model is not ideal. Therefore, it is necessary to further group and verify the data by city scale, as the relationship between the \(D_{a}\) value and city scale may not exhibit a simple linear pattern. According to China's classification standards for city sizes, the 60 experimental group cities are divided into four categories based on urban population size: 0-0.2, 0.2-0.5, 0.5-1, and over 1 million. The average \(D_{a}\) values for each group of cities were calculated separately, as shown in Table 3 and Figure 6. \begin{table}
\begin{tabular}{c c c c c} \hline
**Administrative Level** & **Average Value of \(D_{aR}\)** & **Average Value of \(D_{aE}\)** & **Average Value of \(D_{aG}\)** & **Average Value of \(D_{aL}\)** \\ \hline Prefecture-level cities & 0.0606 & 0.0777 & \(-0.0839\) & \(-0.0014\) \\ County-level cities & 0.0047 & 0.0033 & 0.0389 & 0.0378 \\ and counties & & & & \\ \hline \end{tabular}
\end{table} 
Table 2: The average performance of \(D_{a}\) values for different indicators in cities of varying administrative levels. \begin{table}
\begin{tabular}{c c c c c} \hline
**City Size** & **Average Value of \(D_{aR}\)** & **Average Value of \(D_{aE}\)** & **Average Value of \(D_{aG}\)** & **Average Value of \(D_{aL}\)** \\ \hline
0–0.2 & \(-0.0542\) & \(-0.1311\) & 0.4363 & \(1.1551\) \\
0.2–0.5 & 0.9794 & 0.5602 & \(1.6618\) & \(0.1472\) \\
0.5–1 & 0.4894 & 0.9420 & \(1.1322\) & \(-0.3139\) \\ above 1 & 0.8236 & \(1.4297\) & \(-5.1937\) & \(-0.0929\) \\ \hline \end{tabular}
\end{table} 
Table 3: The average performance of \(D_{a}\) values for different indicators in cities of varying sizes. The results show that HSR is detrimental to population aggregation in small cities with fewer than 200,000 people, affecting both resident and employment populations. For cities with populations over 200,000, the effects differ. For resident population, HSR most effectively promotes population aggregation in cities with populations between 200,000 and 500,000, followed by those with populations over 1 million. In contrast, for employment population, the larger the city, the more pronounced the positive effect of HSR. This  
Figure 5: Scatter plot and linear regression equation of city size and \(D_{a}\) indicators. Figure 6: The average performance of \(D_{a}\) values for different indicators in cities of varying sizes. suggests that under the influence of HSR, medium-sized cities have the opportunity to gain an advantage in resident population aggregation, while larger cities are better positioned to benefit from employment population aggregation. Regarding economic growth, HSR has a significant positive effect on medium and small cities with populations under 1 million, but the effect is reversed for larger cities with populations over 1 million. This may be because large cities along the three lines are generally more developed and have entered a stage of high-quality development, focusing less on rapid economic growth. In contrast, nearby control cities are still in the \"catch-up\" phase, pursuing faster economic growth.