## 4 Results
### Comparison of the Accuracy of Regression Analysis Models  
Based on the parameter optimization findings, an MPA-XGBoost model featuring a swarm size of 60 was selected for further analysis. The regression models concerning the PC and multi-factor indicators of the mining stope were evaluated using the test dataset. These models were subsequently compared with the outcomes derived from the standard XGBoost model, the PSO-XGBoost model, and the widely used regression-based machine learning method, SVM. As shown in Figure 7a-d, a comparative analysis of regression accuracy across different models is provided. The data points that are nearer to the function line (y = x) indicate smaller differences between the predicted and actual values, suggesting a higher level of model accuracy. Moreover, a greater concentration of data points within the \(\pm\)20% error margin is indicative of superior model performance. The MPA-XGBoost model demonstrates the most favorable evaluation metrics in the analysis of PC, as depicted in Figure 7a. Its \(R^{2}\) value reaches 0.958, surpassing all other models, which clearly indicates a robust correlation between the predicted data and the actual data in the regression analysis. In addition, the _VAF_ attains a high value of 95.981, ranking first among all regression methods, which vividly illustrates the remarkable explanatory power of the MPA-XGBoost model for the dataset. This results in highly reliable regression analysis outcomes. Moreover, both the _MAE_ and _RMSE_ values are minimized in \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline num\_trees & 997 \\ max\_depth & 8 \\ eta & 0.0650 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optimal calculation parameters. Figure 7: Comparison of regression models. the MPA-XGBoost model. Such minimization highlights the model's outstanding ability to effectively capture the nonlinear patterns embedded within the PC dataset. Compared with the traditional XGBoost prediction model, the MPA-XGBoost and PSO-XGBoost models demonstrate superior accuracy, as illustrated in Figure 7b,c. These findings highlight that incorporating population-based optimization algorithms enables more precise parameter tuning for XGBoost, leading to substantial improvements in the overall performance of the regression analysis model. Furthermore, the selection of optimization techniques plays a critical role in the parameter adjustment process within XGBoost. Notably, the MPA exhibits a better performance than the PSO algorithm during optimization. This is attributed to the tendency of the PSO algorithm to prematurely converge to local optima, whereas the MPA shows stronger global optimization capabilities. When compared with conventional machine learning methods (as shown in Figure 7d), the MPA-XGBoost model demonstrates significant improvements in both regression analysis accuracy and associated error metrics. This model is capable of accurately capturing the complex relationships between PC and multiple influencing factors. Moreover, unlike traditional approaches, it optimizes the parameter selection process, thereby enhancing usability. In conclusion, when benchmarked against standard machine learning models, this approach achieves superior performance in terms of computational efficiency. The Taylor diagram (Figure 7e) is developed based on the mean square deviation (\(SD\)), \(RMSE\), and \(R^{2}\) values of the four models [38]. The reference point REF, defined by a standard deviation (\(SD=3\)), root mean square error (\(RMSE=6\)), and coefficient of determination (\(R^{2}=1\)), established a rigorous and representative performance benchmark. This benchmark integrates critical dimensions such as data dispersion, prediction error, and goodness of fit, providing a robust quantitative foundation for objectively assessing the prediction accuracy of various models.