## 4 Results
### Models and Statistical Validation
However, when the presence of outliers is considered, SET-2 shows a better performance, as it has fewer outliers in the distribution. Figure 9 shows a comparison of the SVMR models with the optimal regularization parameters presented in Table 8. The results follow the same behavior, with all sets reaching very good results in the combined performance (above 83%), except for SET-1 and SET-4. The model that uses predictors from SET-3, obtained via recursive variable elimination, was selected with a regularization hyperparameter value of 2 and a bandwidth hyperparameter value of 0.05. Under the criteria of higher AUC and lower error rate, this model achieved the best score, with an AUC value of 94.86% and an error rate of 10.56%. Under the combined performance criteria, the best model is SET-3, as it has the highest value (84.84%). The second-best model corresponds to the model that uses all the variables (SET-6), with an AUC value of 94.70% and an error rate of 11.72%. Under the combined performance criteria, the model that uses SET-6 remains in second place. Therefore, both criteria coincide with the selection of the first- and second-best models, as the SET-3 model performs better in both performance measures in terms of AUC, error, and combined performance. This \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Predictor**} & **Regularization** & \multirow{2}{*}{**Average AUC (\%)**} & **Average Error** & **Combined** \\  & **Parameter** & & **Rate (\%)** & **Performance (\%)** \\ \hline SET-1 & 0.03 & 92.17 & 14.86 & 78.47 \\ SET-2 & 0.44 & 94.11 & 12.71 & 82.15 \\ SET-3 & 1.88 & 94.03 & 13.16 & 81.66 \\ SET-4 & 0.003 & 87.86 & 20.55 & 69.81 \\ SET-5 & 0.50 & 94.11 & 12.83 & 82.03 \\ SET-6 & 1.09 & 93.89 & 13.03 & 81.66 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Optimal hyperparameter values for each of the SVML models created from the training data and combined performance metric. Figure 8: Box-plot showing performance comparison of SVML models for each predictor set with training data, comparing the AUC and error rate of each, to select the best submodel. decision is further validated by analyzing the boxplot of the models in shown Figure 9. The SET-3 model is observed to have a more concentrated distribution, with values closer to an AUC of 0.95 and an error of around 0.1, while the points representing the SET-6 model are more dispersed, covering a wider range in both AUC and error rates. Therefore, the SET-3 model has less dispersion in both AUC and error than the SET-6 model, indicating that the AUC and error values of the SET-3 models are more consistent and closer to each other. Tables 9 and 10 show the optimized hyperparameter values of the models with principal components and performance metrics, respectively, for the dataset provided by the PCA. The best model according to the criteria of the highest AUC and lowest error rate corresponds to the ANN (ann_cp) since its error rate is 10.10% and its AUC is 95.40%, making it the best model. When the training results are analyzed based on the combined performance criterion, the ANN also shows the highest value in this metric (85.80%). Both metrics show that the ANN using principal components has the highest performance. The second-best model in the training phase is RF (rf_cp), as it has an AUC of 95.31% and an error rate of 11.0%, leading to lower combined performance (84.80%). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Predictor**} & **Regularization** & **Kernel** & **Average** & **Average Error** & **Combined** \\  & **Parameter** & **Bandwidth** & **AUC (\%)** & **Rate (\%)** & **Performance (\%)** \\ \hline SET-1 & 1.90 & 0.05 & 93.83 & 13.41 & 81.24 \\ SET-2 & 1.95 & 0.05 & 94.48 & 12.03 & 83.11 \\ SET-3 & 2.00 & 0.05 & 94.86 & 10.56 & 84.84 \\ SET-4 & 1.80 & 0.05 & 91.17 & 17.07 & 75.61 \\ SET-5 & 2.00 & 0.05 & 94.39 & 11.92 & 83.14 \\ SET-6 & 2.00 & 0.05 & 94.70 & 11.72 & 83.60 \\ \hline \hline \end{tabular}
\end{table}