## 3 Results and Discussion
### Multiple Linear Regression  
An MLR model was employed to predict the peak and residual interface shear strength, as detailed in Table 4, which presents metrics derived from the training, testing, and 10-fold cross-validation (CV) datasets for both peak and residual shear stress.  
For peak shear stress, the model's Mean Absolute Error (MAE) indicated higher accuracy during the training phase with a value of 2.98, compared to the testing and cross-validation phases, which scored 3.62 and 3.45, respectively. The Root Mean Square Error (RMSE) exhibited a similar trend, with the training phase achieving the lowest error at 3.93, followed by the cross-validation phase at 4.47, and the testing phase at 4.53. The Root Mean Squared Logarithmic Error (RMSLE) remained consistent between the training and testing phases, both at 0.18 and 0.19, while the cross-validation phase presented a slightly higher error of 0.21. The R\({}^{2}\) values reflected the model's robustness, showing a high degree of fit at 0.92 in the training phase, and a slightly lower yet comparable 0.90 in both the testing and  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Training Database**} & **Testing Database** & **10-Fold CV** \\ \hline \multirow{5}{*}{\(\text{RMSE}^{\text{\text{\text{\text{\text{\text{\textasci  
cross-validation phases. These results are visually represented in Figure 12. The empirical equation for estimating the \(\tau_{\text{P}}\) is given by the following equation.  
\[\tau_{\text{P}}=-63.446-(39.664\times\text{RI})-(4.352\times\text{D}_{50})+(11.4 1\times\text{n})-(8.539\times\text{C}_{\text{u}})+(95.063\times\text{C}_{\text{c} })+\] \[(0.176\times\text{R}_{\text{t}})-(0.008\times\text{HD})+(0.428 \times\sigma)\]  
where \(\tau_{\text{P}}\) is the peak interface shear strength, \(RI\) is the particle regularity, \(\text{D}_{50}\) is the mean particle size, \(\text{n}\) is the porosity, \(\text{C}_{\text{u}}\) is the coefficient of uniformity, \(\text{C}_{\text{c}}\) is the coefficient of curvature, \(\text{R}_{\text{t}}\) is surface roughness, HD is surface hardness, and \(\sigma\) is the normal stress.  
For residual shear stress, the MAE values were 3.61 for the training phase, 3.39 for the testing phase, and 3.45 for the cross-validation phase. The RMSE values followed a similar pattern, with 4.72 for the training phase, 4.52 for the testing phase, and 4.47 for the cross-validation phase. The RMSLE values were 0.23 for the training phase, 0.19 for the testing phase, and 0.21 for the cross-validation phase. The \(\text{R}^{2}\) values were slightly lower compared to the peak shear stress, with 0.89 for both the training and testing phases and 0.90 for the cross-validation phase. These results are illustrated in Figure 13. The empirical equation for estimating the \(\tau_{\text{r}}\) is given by the following equation.  
\[\tau_{\text{r}}=-123.316-(48.287\times\text{RI})-(3.489\times\text{D}_{50})+(9.889\times\text{n})-(13.534\times\text{C}_{\text{u}})+(167.996\times\text{C}_{ \text{c}})\] \[+(0.096\times\text{R}_{\text{t}})-(0.002\times\text{HD})+(0.416 \times\sigma)\]  
The model performed well due to high-quality data and effective feature selection, with low errors in peak and residual shear stress predictions. This highlights the model's accuracy and robustness.  
Figure 12: Comparison of actual and predicted peak interface shear strength using MLR for (**a**) the training dataset, (**b**) the testing dataset, and (**c**) 10-fold cross-validation.