## 5 Results and Discussion
Figure 8f,g show residuals  
Figure 7: Comparison between the Taylor plot for each model. (**a**) Linear Regression, (**b**) Random Forest, (**c**) Gradient Boosting, (**d**) XGBoost, (**e**) LightGBM, (**f**) SVM-SVR, and (**g**) MLP-ANN. for the SVM-SVR and MLP-ANN models, respectively, with wider spreads compared to the boosting methods but narrower than Linear Regression and Random Forest. The SVM-SVR residuals are fairly symmetrical around the mean, implying balanced prediction errors, while MLP-ANN shows a right-skewed distribution, indicating a tendency towards overprediction. Figure 9 illustrates the residuals of predicted versus actual UCS values for seven different models. Residuals are the differences between observed values and the values predicted by the models, and analyzing these residuals helps evaluate model performance by identifying any patterns or biases in the predictions. As demonstrated in Figure 9, in the Linear Regression model, the residuals exhibit a noticeable spread around the zero line, with a tendency to increase as the actual UCS values increase. This pattern suggests that the model may be underpredicting for higher UCS values and overpredicting for lower UCS values, indicating a potential linear bias in the predictions. Figure 9 shows residuals that are more tightly clustered around the zero line compared to Linear Regression, although there are still some noticeable outliers. The residuals do not display a clear pattern, indicating that Random Forest provides a more balanced prediction across the range of UCS values but still has room for improvement in reducing prediction errors. Figure 9 presents residuals that are fairly well distributed around the zero line, with fewer outliers than both Linear Regression and Random Forest. This indicates that Gradient Boosting has a  
Figure 8: Comparison between the residual distribution of each model. (**a**) Linear Regression, (**b**) Random Forest, (**c**) Gradient Boosting, (**d**) XGBost, (**e**) LightGBM, (**f**) SVM-SVR, and (**g**) MLP-ANN. strong predictive capability and effectively minimizes bias, providing accurate predictions across the range of UCS values. As illustrated in Figure 9d, XGBoost also exhibits a well-distributed pattern of residuals around the zero line, similar to Gradient Boosting. The absence of a clear trend or bias in the residuals further confirms XGBoost's robustness and accuracy in predicting UCS values. As depicted in Figure 9e, the LightGBM model displays residuals that are somewhat more scattered, with a few noticeable outliers, particularly at the higher UCS values. While LightGBM generally performs well, these outliers suggest occasional overprediction or underprediction, indicating variability in the model's accuracy. Figure 9f shows a relatively balanced distribution of residuals around the zero line, although there are several instances of significant positive and negative residuals. This suggests that while SVM-SVR can predict UCS values with reasonable accuracy, it may struggle with certain data points, leading to occasional large errors. Figure 9g reveals residuals that are spread more widely around the zero line, with several outliers, especially at the lower end of the UCS range. This dispersion indicates that MLP-ANN has difficulty maintaining consistent prediction accuracy across the range of UCS values, resulting in higher variability in its predictions. The residual analysis in Figure 9 highlights that ensemble methods such as Gradient Boosting and XGBoost provide the most accurate and unbiased predictions, with residuals closely clustered around the zero line and minimal outliers. Random Forest and LightGBM also perform well but exhibit slightly more variability. Linear Regression and MLP-ANN show higher dispersion and noticeable patterns in residuals, indicating potential biases and less reliable predictions. SVM-SVR offers reasonable accuracy but with occasional large residuals. Figure 9: Comparison between the residuals of each model versus the actual UCS values.