## 5 Results and Discussion
As shown in Figure 7d, the XGBoost model also exhibits a high correlation coefficient, similar to Gradient Boosting, and a standard deviation that closely matches the observed values. This indicates that XGBoost is highly effective in predicting UCS values with a high degree of accuracy and reliability. As depicted in Figure 7e, LightGBM shows a strong correlation coefficient, slightly less than that of Gradient Boosting and XGBoost, but still indicative of a good predictive performance. The standard deviation is close to the observed values, although there is a slight deviation, suggesting some minor discrepancies in capturing the full range of data variability. Figure 7f presents a good correlation coefficient for the SVM-SVR model, although not as high as the ensemble methods like Gradient Boosting and XGBoost. The standard deviation is comparable to the observed values, indicating that SVM-SVR performs well in terms of capturing data variability, albeit with occasional prediction inaccuracies. Figure 7g shows a strong correlation coefficient and a standard deviation that aligns well with the observed values, indicating that MLP-ANN captures both the trend and variability in the UCS data effectively. However, similar to SVM-SVR, it might have occasional outliers or prediction errors. The analysis of residual distributions for various machine learning models is critical for understanding their predictive performance. Residuals, which are the differences between observed and predicted values, should ideally exhibit a random pattern centred around zero; any discernible trends or patterns may suggest that the model is not effectively capturing underlying relationships within the data. This analysis is instrumental in identifying biases in the model, revealing whether it tends to consistently overestimate or underestimate predictions. Moreover, it helps to detect non-linearities that may require additional features or interaction terms for better representation. Assessing the residuals also aids in evaluating the homogeneity of variance; the presence of heteroscedasticity can compromise the reliability of the model's predictions. Figure 8 presents the residual distributions of seven different models. As shown in Figure 8a, Linear Regression demonstrates a wide spread of residuals, with several outliers on both ends. The distribution appears slightly skewed to the left, indicating that the model tends to underpredict in some instances. The presence of multiple residual peaks suggests that the model might not fully capture the underlying data patterns, leading to heterogeneous residuals. As depicted in Figure 8b, the Random Forest technique shows a more centred residual distribution, although it still exhibits some degree of skewness to the left. The residuals are more tightly clustered around the mean compared to Linear Regression, suggesting better overall pre  
Figure 6: Comparison between the relative importance of the inputs for each model. (**a**) Linear Regression, (**b**) Random Forest, (**c**) Gradient Boosting, (**d**) XGBoost, (**e**) LightGBM, (**f**) SVM-SVR, and (**g**) MLP-ANN. dictive accuracy. However, the model still struggles with extreme values, as evidenced by the residuals extending far from the mean. Figure 8c,d present similar residual distributions for the Gradient Boosting and XGBoost models, respectively, with both showing a noticeable concentration around the mean and a reduction in extreme residuals. This indicates that these models are effective in minimizing prediction errors and handling variance within the data. Both distributions, however, show slight left skewness, suggesting occasional underpredictions. As demonstrated in Figure 8e, the LightGBM model displays a distinctive pattern with a significant peak around a small positive residual value. This indicates a slight bias in the model's predictions, consistently overestimating to a small extent. Despite this, the distribution is relatively narrow, suggesting high accuracy in most predictions.