## 5 Statistical Analysis  
Statistical analysis of the SDMT results was carried out using the Statistica software version 12 [54; 55; 56]. Models of linear and nonlinear regression were analyzed [57]. The analyzed data set comprised the \(P=16\) pattern described by one dependent variable the normalized undrained shear strength \(Y=\tau_{fu}\)/\(\sigma^{{}^{\prime}}v\in\{\)0.803-2.382\(\}\), and four independent variables: The normalized net value of the corrected first pressure reading \(X_{1}=(p_{o}-u_{o})\)/\(\sigma^{{}^{\prime}}v\in\{\)4.301-13.743\(\}\); the normalized net value of the corrected second pressure reading \(X_{2}=(p_{1}-u_{o})\)/\(\sigma^{{}^{\prime}}v\in\{\)9.222-27.525\(\}\); the normalized difference between corrected second pressure reading and the corrected first pressure reading \(X_{3}=(p_{1}-p_{o})\)/\(\sigma^{{}^{\prime}}v\in\{\)3.559-13.782\(\}\); and the normalized shear wave velocity \(X_{4}=V_{s}\)/100 \(\in\{\)1.750-4.240\(\}\), selected from the variables presented in Table 4.  
Simple regression models were considered:  
\[y=a\ +bx\pm SEE \tag{12}\]  
where \(a\) is intercept of line, \(b\) is slope of line, and \(SEE\) is the standard error of estimation. In the case when measurement of the shear wave velocity \(V_{s}\) was not carried out, the \(\tau_{fu}\)/\(\sigma^{{}^{\prime}}v\) can be evaluated using simple linear regressions shown as Equation (13) or Equation (14), which explain 85.5% and 83.1% of the variability of \(Y=\tau_{fu}\)/\(\sigma^{{}^{\prime}}v\), respectively (Table 6). Plots of regression lines (13) and (14) with 95% confidence intervals are given in Figure 8. The simple linear regression models (15) and (16) shown in Table 6 gave worse accuracy. \begin{table} \begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{Model} & \multirow{2}{*}{Equation Formula/No.} & \multicolumn{3}{c}{Determination} & \multirow{2}{*}{Max \(RE\) (\%)} & \multirow{2}{*}{Mean \(RE\) (\%)} \\  & & & \(R^{2}\) (\(c\)) & & \\ \hline \multirow{4}{*}{Simple linear regressions} & \(\tau_{fu}\)/\(\sigma^{{}^{\prime}}v=0.3023+0.1442((p_{o}-u_{o})\sigma^{{}^{\prime}}v)\) (13)\({}^{*}\) & 0.855 & 0.2089 & 41.0 & 12.4 \\ \cline{1-1} \cline{2-6}  & \(\tau_{fu}\)/\(\sigma^{{}^{\prime}}v=0.4513+0.0698((p_{1}-u_{o})\sigma^{{}^{\prime}}v)\) (14)\({}^{**}\) & 0.831 & \(\pm\)0.2262 & 37.7 & 13.0 \\ \cline{1-1} \cline{2-6}  & \(\tau_{fu}\)/\(\sigma^{{}^{\prime}}v=0.6652+0.1258((p_{1}-p_{o})\sigma^{{}^{\prime}}v)\) (15)\({}^{**}\) & 0.751 & \(\pm\)0.2747 & 39.4 & 15.0 \\ \cline{1-1} \cline{2-6}  & \(\tau_{fu}\)/\(\sigma^{{}^{\prime}}v=-0.1159+0.5178(v/100)\) (16)\({}^{*}\) & 0.757 & \(\pm\)0.2714 & 33.0 & 12.0 \\ \hline \hline \end{tabular}   
* * *—coefficient \(a\) is statistically non-significant, ***The linear two-factor regression model was in the form of:  
\[y=a_{o}+a_{1}x_{1}+a_{2}x_{2}\pm SEE \tag{17}\]  
where \(a_{0}\), \(a_{1}\), and \(a_{2}\) are regression coefficients. The non-linear two-factor regression model was adopted based on the analysis of the curve shape and scatterplots of variables. Among the linearized models, i.e., those that can be reduced to a linear form by appropriate transformation of variables or parameters, the power function of the form was selected:  
\[y=\beta_{o}\cdot x_{1}\beta_{1}\cdot x_{2}\beta_{2} \tag{18}\]  
Logarithmic transformation was applied and a transformed regression model was obtained:  
\[log\ y=log\ \beta_{o}+\beta_{1}\cdot log\ x_{1}+\beta_{2}\cdot logx_{2} \tag{19}\]  
The non-linear two-factor regression was considered as the best model. The fulfilment of statistical assumptions (e.g., normality of residual distribution and residuals analysis) was checked.