# Analysis of Ground Subsidence Vulnerability in Urban Areas Using Spatial Regression Analysis
## 3 Data Correlation Analysis  
To derive the attribute information of underground utilities that affected ground subsidence involving six types of underground utilities, Pearson correlation analysis was conducted between the presence, density, diameter, average depth, and age of the six types of underground utilities, the density of all six types of underground utilities, and the occurrence of ground subsidence. Correlation analysis is an analysis that determines the degree of the linear relationship between independent and dependent variables, and the correlation coefficient has a value between \(-1\) and \(1\). The correlation coefficient between the variables can be calculated through Equations (1) and (2) [17; 18]. \[\text{Corr}(\text{X},\text{Y})=\rho(\text{X},\text{Y})=\frac{\text{Cov}(\text{X },\text{Y})}{\sigma_{\text{x}}\sigma_{\text{y}}} \tag{1}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Category** & **MIN** & **MAX** & **M** & **SD** \\ \hline \multirow{4}{*}{Water pipeline} & Density & 0.00 & 0.08 & 0.03 & 0.02 \\  & Diameter (cm) & 15.00 & 2400.00 & 318.77 & 417.83 \\  & Average depth (m) & 0.10 & 25.00 & 1.44 & 0.76 \\  & Age (years) & 1.00 & 68.00 & 28.18 & 11.05 \\ \hline \multirow{4}{*}{Sewer pipeline} & Density & 0.00 & 0.05 & 0.02 & 0.01 \\  & Diameter (cm) & 150.00 & 3000.00 & 609.45 & 231.36 \\  & Average depth (m) & 0.02 & 21.55 & 1.27 & 1.03 \\  & Age (years) & 2.00 & 77.00 & 40.92 & 27.30 \\ \hline \multirow{4}{*}{Power cable} & Density & 0.00 & 0.05 & 0.01 & 0.01 \\  & Diameter (cm) & 50.00 & 300.00 & 164.72 & 27.12 \\  & Average depth (m) & 0.10 & 11.00 & 1.14 & 0.50 \\  & Age (years) & 1.00 & 42.00 & 11.62 & 7.63 \\ \hline \multirow{4}{*}{Communication} & Density & 0.00 & 0.09 & 0.02 & 0.01 \\  & Diameter (cm) & 1.00 & 1000.00 & 92.16 & 18.51 \\  & Average depth (m) & 0.20 & 1500.00 & 2.42 & 39.30 \\  & Age (years) & 1.00 & 63.00 & 29.51 & 11.48 \\ \hline \multirow{4}{*}{Heating pipeline} & Density & 0.00 & 0.07 & 0.00 & 0.01 \\  & Diameter (cm) & 20.00 & 1100.00 & 322.17 & 230.68 \\  & Average depth (m) & 0.50 & 6.70 & 1.48 & 0.28 \\  & Age (years) & 2.00 & 38.00 & 20.81 & 10.10 \\ \hline \multirow{4}{*}{Gas pipe} & Density & 0.00 & 0.06 & 0.02 & 0.01 \\  & Diameter (cm) & 20.00 & 750.00 & 162.62 & 93.78 \\ \cline{1-1}  & Average depth (m) & 0.10 & 6.50 & 1.10 & 0.50 \\ \cline{1-1}  & Age (years) & 1.00 & 49.00 & 25.28 & 8.99 \\ \hline \multirow{4}{*}{All six types of underground facilities} & The density of all six types of types of underground facilities & 0.00 & 0.25 & 0.09 & 0.05 \\ \cline{1-1}  & Density & 0.00 & 0.06 & 0.02 & 0.01 \\ \cline{1-1}  & Diameter (cm) & 20.00 & 750.00 & 162.62 & 93.78 \\ \cline{1-1}  & Average depth (m) & 0.10 & 6.50 & 1.10 & 0.50 \\ \cline{1-1}  & Age (years) & 1.00 & 49.00 & 25.28 & 8.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of the data. \[\mathrm{r}=\frac{\mathrm{s_{xy}}}{\mathrm{s_{x}}\mathrm{s_{y}}}=\frac{\sum_{i=1}^{ \mathrm{n}}(X_{i}-\bar{X})\bigg{(}Y_{i}-\bar{Y}\bigg{)}}{\sqrt{\sum_{i=1}^{n} \left(X_{i}-\bar{X}\right)^{2}\sum_{i=1}^{n}\left(Y_{i}-\bar{Y}\right)^{2}}} \tag{2}\]  
\(\mathrm{s_{xy}}\): Covariance of X and Y variables, \(\mathrm{s_{x}}\): standard deviation of variable X, \(\mathrm{s_{y}}\): and standard deviation of variable Y. After obtaining the correlation coefficient, hypotheses of correlation in the population through Equation (3) were conducted to determine whether the correlation coefficient between two variables is statistically significant. If the test statistic is less than or equal to 0.05, there is a significant correlation between the two variables [19; 20]. \[\mathrm{t}=r\sqrt{\frac{\mathrm{n}-2}{1-\mathrm{r}^{2}}} \tag{3}\]  
Table 2 presents the results of the Pearson correlation analysis.