# Regression Equations for Estimating Landslide-Triggering Factors Using Soil Characteristics
## 3 Results
### Derivation of Regression Equations for Evaluating Landslide-Triggering Factors
#### 3.5.2 Regression Equations of Shear Strength  
To estimate the shear strength of soil in various geological features through the regression equation, the researchers used correlation analysis using various soil tests and analytical data on samples collected in the study sites similar to the estimation of the permeability coefficient. Pearson correlation analysis was conducted on the soil variables of 16 properties to select properties that are significant for shear strength with cohesion and internal friction angle. Pearson's correlation coefficient and significance were obtained for cohesion and internal friction angle of soil, as shown in Table 4. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Geology**} & \multirow{2}{*}{**Soil Variable**} & \multicolumn{2}{c}{**Unstandardized Coefficients**} & \multicolumn{2}{c}{**Standardized**} & \multirow{2}{*}{**t-value**} & \multirow{2}{*}{**Significance**} \\  & & & & **Coefficients** & & \\ \cline{3-6}  & \multirow{2}{*}{**B**} & **Standard** & & & **Brea** & \\ \hline \multirow{4}{*}{**Gneiss**} & (Constant) & \(-1.893\times 10^{-2}\) & 0.004 & & \(-5.004\) & 0.000 \\ \cline{2-6}  & Effective grain size, \(\mathrm{D}_{10}\) & \(1.076\) & 0.161 & 0.774 & 6.683 & 0.000 \\ \cline{2-6}  & Coefficient of uniformity, \(c_{u}\) & \(-1.629\times 10^{-4}\) & 0.000 & \(-0.151\) & \(-1.350\) & 0.185 \\ \cline{2-6}  & Void ration, \(e\) & \(1.488\times 10^{-2}\) & 0.002 & 0.655 & 9.415 & 0.000 \\ \hline \multirow{4}{*}{**Granite**} & (Constant) & \(-9.907\times 10^{-3}\) & 0.001 & & \(-7.831\) & 0.000 \\ \cline{2-6}  & Effective grain size, \(\mathrm{D}_{10}\) & \(8.281\times 10^{-3}\) & 0.001 & 0.474 & 9.177 & 0.000 \\ \cline{1-1} \cline{2-6}  & Coefficient of uniformity, \(c_{u}\) & 0.639 & 0.047 & 0.772 & 13.702 & 0.000 \\ \cline{1-1} \cline{2-6}  & Void ration, \(e\) & \(-2.766\times 10^{-5}\) & 0.000 & \(-0.058\) & \(-0.973\) & 0.340 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Statistical results of permeability coefficient by the regression analysis of soils by different geological feature. For the genesis region, the soil properties with a high significance level for cohesion were fine grain content and uniformity coefficient. Therefore, the two were selected as independent variables for regression analysis. Meanwhile, the soil properties that produced high significance for internal friction angle were void ratio, saturation unit weight, and dry unit weight. As the saturation unit weight and dry unit weight are proportional to each other, only void ratio and dry unit weight were selected as independent variables to be applied to the regression analysis to simplify the equation. The properties with a high significance level to cohesion in granite soils were found to be as follows: fine-grain soil content, saturation, effective diameter, and uniformity coefficient. Among these properties, the significance of the equality coefficient was 0.086, which is greater than the significant level of 0.05 from a statistical point of view, leading to the exclusion of the equality coefficient from the equation, and adding the degree of saturation and effective diameter instead. Finally, only fine-grained