## 3 Results
### Random Forest Analysis  
Table 5 outlines the input factors and key parameter settings of the RF model. This model utilizes eight input factors: gender, smoking status, alcohol consumption, voice user status, coffee consumption, comorbidity, surgery status, and voice training status. The parameter configuration includes an n_estimators value of 50, indicating that the model comprises 50 decision trees. The max_depth parameter is set to none, allowing each tree to grow to its maximum depth. The min_samples_split and min_samples_leaf are set to 2 and 1, respectively, specifying the minimum number of samples required to split an internal node and to be present at a leaf node. Additionally, max_features is configured as sqrt, meaning the number of features considered for splitting each node is the square root of the total number of features. The bootstrap parameter is set to true, indicating that each tree is trained using bootstrap samples.  
Table 6 illustrates the confusion matrix, demonstrating the predictive performance of the model, while Table 7 summarizes the classification metrics. The model achieves an overall accuracy of 84.61%, with a high precision of 0.88, indicating that 88% of cases predicted as \"VHI +\" are true positives. However, the specificity is 0%, revealing that the model fails to correctly identify any \"VHI -\" instances. Conversely, the recall is 0.95, showing that the model successfully identifies most actual \"VHI +\" cases. The F-score of 0.91 suggests that the model maintains a good balance between precision and recall. These results indicate that while the model performs well in predicting \"VHI +\", its performance in predicting \"VHI -\" is notably poor. This could be attributed to data imbalance, where the limited number of \"VHI -\" cases may hinder the model's ability to accurately detect negative instances.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Dependent Variable** & **Independent Variable** & **B** & **S.E.** & _Wald_ & _p Value_ & _Exp(B)_ \\ \hline \multirow{8}{*}{VHI} & gender & **3.220** & **1.275** & **6.381** & **0.012** & **25.033** \\  & smoking status & 1.175 & 1.602 & 1.224 & 0.263 & 3.237 \\  & alcohol consumption & 0.324 & 0.972 & 0.111 & 0.739 & 1.382 \\  & voice user status & \(-\)1.916 & 1.043 & 3.372 & 0.066 & 0.147 \\  & coffee consumption & \(-\)1.330 & 1.277 & 1.084 & 0.298 & 0.265 \\  & comorbidity & \(-\)0.313 & 0.964 & 0.106 & 0.745 & 0.731 \\  & surgery status & \(-\)1.757 & 1.187 & 2.190 & 0.139 & 0.173 \\  & voice training status & \(-\)0.405 & 1.054 & 0.147 & 0.701 & 0.667 \\ \hline \multirow{3}{*}{Model} & \multicolumn{5}{c}{Nagelkerke R\({}^{2}\) = 0.422, \(p\) = 0.006} \\  & & \multicolumn{5}{c}{Hosmer–Lemeshow test \(p\) = 0.967} \\ \cline{1-1}  & & \multicolumn{5}{c}{Classification accuracy: 91.2\%} \\ \hline \hline \end{tabular}
\end{table}
Table 4: _p_-values calculated for various factors.  
\begin{table}
\begin{tabular}{c c} \hline \hline  & Gender, Smoking Status, Alcohol Consumption, Voice User \\ Input Factors & Status, Coffee Consumption, Comorbidity, Surgery Status, \\  & and Voice Training Status \\ \hline n\_estimators & 50 \\ max\_depth & None \\ min\_samples\_split & 2 \\ min\_samples\_leaf & 1 \\ max\_features & sqrt \\ bootstrap & True \\ \hline \hline \end{tabular}
\end{table}
Table 5: Parameter setting information related to RF modeling.