## 3 Results
### XGBoost Model Evaluation
The optimal feature combination of the LOG(PERM) model is [AC, CAL, CNL, DEN, SP, RLLS, PE, GR, RLLD], and after the hyper-parameter optimization step, the MAE of the training set is 0.0205, that of the test set is 0.3543, that of the training set R\({}^{2}\) is 0.99, and that of the test set R\({}^{2}\) is 0.62. The optimal feature combination of the Arctan(PERM) model is [CAL, CNL, DEN, SP, PE, GR, RLLD], and after the hyper-parameter optimization step, the MAE of the training set is 0.0225, and that of the test set is 0.0893; the R\({}^{2}\) of the training set is 0.96, and that of the test set is 0.52. The effect of fitting the model test and prediction sets is shown in Figure 5, where the POR and LOG(PERM) models are insignificantly overfitted and the PERM and Arctan(PERM) models are significantly overfitted. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Algorithm** & **Feature Combination** & \begin{tabular}{c} **Hyper-Parameter** \\ **Values** \\ \end{tabular} & \begin{tabular}{c} **MAE of** \\ **Training Set** \\ \end{tabular} & \begin{tabular}{c} **MAE of** \\ **Test Set** \\ \end{tabular} & \begin{tabular}{c} **R\({}^{2}\) of** \\ **Training Set** \\ \end{tabular} & \begin{tabular}{c} **R\({}^{2}\) of** \\ **Set** \\ \end{tabular} \\ \hline \multirow{3}{*}{POR} & [AC, CAL, CNL, DEN, SP, RLLS, PE, GR] & \begin{tabular}{c} learning\_rate: 0.1 \\ max\_depth: 50 \\ min\_child\_weight: 9 \\ n\_estimators: 300 \\ \end{tabular} & 0.0008 & 0.0671 & 0.98 & 0.72 \\ \hline \multirow{3}{*}{PERM} & [AC, CAL, SP, RLLS, PE, GR, RLLD] & \begin{tabular}{c} n\_estimators: 100 \\ \end{tabular} & 0.0017 & 0.0084 & 0.99 & 0.32 \\ \hline \multirow{3}{*}{LOG(PERM)} & [AC, CAL, CNL, DEN, SP, RLLS, PE, GR, RLLD] & \
\begin{tabular}{c} learning\_rate: 0.02 \\ max\_depth: 90 \\ min\_child\_weight: 9 \\ n\_estimators: 600 \\ \end{tabular} & 0.0205 & 0.3543 & 0.97 & 0.62 \\ \hline \multirow{3}{*}{Arctan(PERM)} & [CAL, CNL, DEN, SP, PE, GR, RLLD] &
\begin{tabular}{c} learning\_rate: 0.02 \\ max\_depth: 50 \\ min\_child\_weight: 9 \\ n\_estimators: 300 \\ \end{tabular} & 0.0225 & 0.0893 & 0.96 & 0.52 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: XGBoost model hyper-parameter preference values. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & \begin{tabular}{c} **Hyper-Parameter** \\ **Optimization** \\ \end{tabular} & \begin{tabular}{c} **Hyper-Parameter** \\ **Description** \\ \end{tabular} \\ \hline \multirow{3}{*}{XGBoost} & learning\_rate & The smaller the learning rate, the smaller the impact of \\  & & each tree, and the more stable the model training \\ \cline{2-3}  & max\_depth & \
\begin{tabular}{c} Control the maximum depth of each tree, with small \\ values, making it difficult for the model to overfit \\ \end{tabular} \\ \cline{2-3}  & min\_child\_weight & Preventing model overfitting on the training set \\ \cline{2-3}  & n\_estimators &
\begin{tabular}{c} The number of decision trees, the more decision trees \\ there are, the better the model performance \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Description of hyper-parameter optimization of XGBoost model.