## 5 Results and Discussion
### Evaluation  
Once the models were established based on the training dataset, their performance needed to re-checked by experimental results, i.e., the testing dataset. For this state, the testing dataset was tested by the developed models. To have a general assessment of the models, a simple ranking and intensity color methods were applied as shown in Table 5 based on the RMSE and R\({}^{2}\) values. Both training and testing processes were evaluated in this section.  
The results of Table 5 revealed that the AI models provided high reliability in predicting GCV in this study. Color intensity showed that the PSO-SVR model with the radial basis kernel function (i.e., PSO-SVR-RBF) reached the highest accuracy on both training and testing datasets. Additionally, the total ranking of 24 was also interpreted the PSO-SVR-RBF performance. With a slightly lighter color intensity and the overall ranking of 20, the PSO-SVR model with polynomial kernel function (i.e., PSO-SVR-P model) yielded somewhat weaker performance than those of the PSO-SVR-RBF model. Among the PSO-SVR models with different kernel functions (i.e., RBF, P, L), the PSO-SVR model with the linear kernel function (i.e., PSO-SVR-L model) provided lowest performance with a total ranking of eight. Its performance was even lower than those of the MLR model (with an overall ranking of 13). The CART and PCA are the models that provided the poor performance in this study, especially is PCA based on the RMSE, R\({}^{2}\) and ranking values in Table 5. Indeed, the PCA model provided the weakest performance with an RMSE of 439.585, R\({}^{2}\) of 0.794, and a total ranking of four. Figures 9-14 show the deviation between the analyzed and predicted values of GCV in the developed models.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \(\vartheta\) & **RMSE** & **R\({}^{2}\)** \\ \hline
1 & 475.018 & 0.755 \\
2 & 432.723 & 0.797 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Performance of the PCA model with various \(\vartheta\).  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{5}{c}{**Training**} & \multicolumn{5}{c}{**Testing**} & \multirow{2}{*}{**Total**} \\ \cline{2-2} \cline{4-9}  & **RMSE** & **R\({}^{2}\)** & **Rank for** & **Rank for R\({}^{2}\)** & **RMSE** & **R\({}^{2}\)** & **Rank for R\({}^{2}\)** & **Rank for R\({}^{2}\)** & **Rank** \\ \hline PSO-SVR-RBF & 196.878 & 0.956 & 6 & 6 & 219.831 & 0.952 & 6 & 6 & 24 \\ PSO-SVR-P & 204.347 & 0.953 & 5 & 5 & 215.767 & 0.950 & 5 & 5 & 20 \\ PSO-SVR-L & 247.581 & 0.933 & 2 & 2 & 254.216 & 0.931 & 2 & 2 & 8 \\ Multiple linear regression (MLR) & 224.283 & 0.945 & 3 & 3 & 225.943 & 0.946 & 4 & 3 & 13 \\ Classification and regression trees (CART) & 200.891 & 0.916 & 4 & 4 & 226.134 & 0.916 & 3 & 3 & 14 \\ Principal component analysis (PCA) & 432.728 & 0.797 & 1 & 1 & 439.585 & 0.794 & 1 & 1 & 4 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The results of the developed GCV predictive models.  
Figure 10: Analyzed versus predicted GCV by the PSO-SVR-P model.  
Figure 9: Analyzed versus predicted GCV by the PSO-SVR-RBF model.  
Figure 11: Analyzed versus predicted GCV by the PSO-SVR-L model.  
Figure 12: Analyzed versus predicted GCV by the MLR model.  
Figure 14: Analyzed versus predicted GCV by the PCA model.  
Figure 13: Analyzed versus predicted GCV by the CART model.