# Regression Equations for Estimating Landslide-Triggering Factors Using Soil Characteristics
## 3 Results
### Derivation of Regression Equations for Evaluating Landslide-Triggering Factors  
#### 3.5.1 Regression Equations of Permeability Coefficient  
To select soil properties significant to the permeability coefficient, the study examined 16 properties for each sample obtained from the test results through the Pearson correlation analysis. As shown in Table 2, the Pearson correlation coefficient (\(r\)) and significance (\(F\)) can explain the correlation quantitatively. According to the Pearson correlation coefficient, the larger the number is and the closer its significance is to 0, the higher the correlation, regardless of whether the correlation is negative or positive. Furthermore, a negative correlation coefficient shows an inversely proportional relation, while a positive coefficient shows the opposite. As presented in Table 3, the soil properties with high significance for the permeability coefficient showed a high correlation with three soil properties, namely effective diameter, uniformity coefficient, and void ratio. Therefore, these properties were selected as independent variables for the regression analysis. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Soil Variable**} & \multirow{2}{*}{**Correlation**} & \multicolumn{2}{c}{**Permeability**} & \multirow{2}{*}{**Soil Variable**} & \multirow{2}{*}{**Correlation**} & \multicolumn{2}{c}{**Permeability**} \\  & & & **Coefficient, cm/s** & & & **Coefficient, cm/s** & \\ \cline{3-8} \cline{8-8}  & & **Gneiss** & **Granite** & & & **Gneiss** & **Granite** \\ \hline \multirow{2}{*}{**Density**} & \(r\) & 0.293 & 0.118 & \multirow{2}{*}{Liquid limit, \%} & \(r\) & \(-\)0.167 & 0.373 \\ \cline{2-8}  & \(F\) & 0.063 & 0.544 & & \(F\) & 0.310 & 0.046 \\ \hline \multirow{2}{*}{**Water Content, \%**} & \(r\) & 0.045 & \(-\)0.003 & \multirow{2}{*}{Plastic limit, \%} & \(r\) & \(-\)0.065 & 0.161 \\ \cline{2-8}  & \(F\) & 0.781 & 0.987 & & \(F\) & 0.694 & 0.404 \\ \hline \multirow{2}{*}{**Void Ratio**} & \(r\) & 0.353 & 0.551 & \multirow{2}{*}{Gravel, \%} & \(r\) & 0.100 & 0.067 \\ \cline{2-8}  & \(F\) & 0.024 & 0.002 & & \(F\) & 0.535 & 0.729 \\ \hline \multirow{2}{*}{**Porosity, \%**} & \(r\) & 0.238 & 0.213 & \multirow{2}{*}{Sand, \%} & \(r\) & 0.139 & 0.124 \\ \cline{2-8}  & \(F\) & 0.134 & 0.266 & & \(F\) & 0.387 & 0.523 \\ \hline \multirow{2}{*}{**Degree of**} & \(r\) & \(-\)0.162 & \(-\)0.229 & \multirow{2}{*}{Fine, \%} & \(r\) & \(-\)0.189 & \(-\)0.315 \\ \cline{2-8}  & \(F\) & 0.311 & 0.231 & & \(F\) & 0.236 & 0.097 \\ \hline \multirow{2}{*}{**Wet unit Weight,**} & \(r\) & \(-\)0.294 & \(-\)0.533 & \multirow{2}{*}{Effective grain size, D\({}_{10}\), cm} & \(r\) & 0.670 & 0.836 \\ \cline{2-8}  & \(F\) & 0.062 & 0.003 & & \(F\) & 0.000 & 0.000 \\ \hline \multirow{2}{*}{**Saturation Unit**} & \(r\) & \(-\)0.270 & \(-\)0.413 & \multirow{2}{*}{Coefficient of uniformity, \(c_{u}\)} & \(r\) & \(-\)0.627 & \(-\)0.591 \\ \cline{2-8}  & \(F\) & 0.088 & 0.026 & & \(F\) & 0.000 & 0.001 \\ \hline \multirow{2}{*}{**Dry Unit weight,**} & \(r\) & \(-\)0.298 & \(-\)0.504 & \multirow{2}{*}{Coefficient of curvature, \(c_{g}\)} & \(r\) & 0.060 & \(-\)0.470 \\ \cline{2-8}  & \(F\) & 0.058 & 0.005 & & \(F\) & 0.711 & 0.010 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Correlation coefficient and significance results between the permeability coefficient and characteristics of the soil through correlation analysis. Using a two-step process in selecting the soil properties related to the permeability coefficient from the correlation coefficients determined through correlation and regression analysis, more accurate correlations were found, and the contribution of each soil property concerning the permeability coefficient is represented numerically as a regression equation. Then, a simple regression analysis was performed by calculating the permeability coefficients in the permeability test using the effective diameter, uniformity coefficient, and the void ratio to derive the statistics-based equations of soil.