## 3 Results
### Multiple Linear Regression  
Three MLR models were developed in this study. The first regression model used soil compaction (depth 0.4-0.5 m) as the output parameter (RSC_04_0.5). The second one used soil compaction (depth 0-0.5 m) as the output parameter (RSC_0_0.5). The third regression model (RSS) used shear stress as the output. All regression models were based on four independent variables (apparent soil electrical conductivity measured at a depth of 0.5 m, apparent soil electrical conductivity measured at a depth of 1 m, magnetic susceptibility measured at a depth of 0.5 m, and magnetic susceptibility measured at a depth of 1 m). Detailed results of the MLR analysis variables are presented in Table 2.  
The constant term (sometimes called the \"intercept\") in a regression model represents the mean value of the response variable when all of the predictor variables in the model are equal to zero.  
The beta coefficient (b coefficient) is the degree of change in the outcome variable for every one unit of change in the predictor variable.  
The \(p\)-values for the coefficients indicate whether these relationships are statistically significant. A low \(p\)-value (<0.05) means that the coefficient is likely not to equal zero. A high \(p\)-value (>0.05) means that we cannot conclude that the explanatory variable affects the dependent variable. A high \(p\)-value is also called an insignificant \(p\)-value.  
MS measured at 0.5 m of depth is a variable for which statistical significance was not confirmed at the \(\alpha\) = 0.05 level in any of the developed models, while magnetic susceptibility measured at a depth of 1 m was a statistically significant trait only in the RSS model. In the RSC_04_0.5 model, the statistically significant traits were ECa0.5 and ECa1. In the RSC_0_0.5 model, the only statistically significant trait was ECa0.5. The statistically significant traits in the RSS model were ECa0.5 and MS1.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Factor**} & \multicolumn{4}{c}{**RSC\_04_0.5**} & \multicolumn{4}{c}{**RSC\_00.5**} & \multicolumn{4}{c}{**RSS\_085**} \\  & \multicolumn{4}{c}{**Constant Term = 1.812**} & \multicolumn{4}{c}{**Constant Term = 1.545**} & \multicolumn{4}{c}{**Constant Term = 124.587**} \\ \cline{2-13}  & **b** & **Standard** & **b** & **Standard** & **b** & **Standard** & **b** & **Standard** & **b** & **Standard** & **b** \\  & **Coefficient** & **Error b** & \(p\)**-Value** & **Significance** & **Coefficient** & **Error b** & \(p\)**-Value** & **Significance** & **Coefficient** & **Error b** & \(p\)**-Value** & **Significance** \\ \hline \hline \multirow{4}{*}{
\begin{tabular}{c} Apparent soil \\ electrical \\ conductivity \\ 0.5 m (ECa0.5) \\ \end{tabular} } & \multirow{4}{*}{0.390} & \multirow{4}{*}{0.094} & \multirow{4}{*}{0.017} & \multirow{4}{*}{+} & \multirow{4}{*}{\(-0.040\)} & \multirow{4}{*}{0.008} & \multirow{4}{*}{\(<\)0.001} & \multirow{4}{*}{+} & \multirow{4}{*}{5.530} & \multirow{4}{*}{1.06  
Based on the outcome from Table 2, and examining only statistically significant traits, multiple regression equations describing each model are as follows:  
\[\text{RSC\_0.4\_0.5}=1.812-(0.045\times\text{ECa0.5})+0.023\times\text{ECa1} \tag{14}\]  
\[\text{RSC\_0\_0.5}=1.545-(0.040\times\text{ECa0.5}) \tag{15}\]  
\[\text{RSS}=124.587+5.530\times\text{ECa0.5}-(18.247\times\text{MS1}) \tag{16}\]  
Error metrics for multiple linear regression models are detailed in Table 3.