## 5 Results and Discussions
The experimental outcomes are reported in Figure 6:1 As can be observed from this table, the proposed ABC-LM-ANN has achieved the most desired predictive accuracy with RMSE = 0.009, MAPE = 10.705%, MAE = 0.007, and R\({}^{2}\) = 0.840. The LM-ANN model is the second-best prediction approach with RMSE = 0.010, MAPE = 12.400%, MAE = 0.008, and R\({}^{2}\) = 0.811, followed by ABC-ANN (RMSE = 0.010, MAPE = 14.029%, MAE = 0.008, and R\({}^{2}\) = 0.792) and RegTree (RMSE = 0.010, MAPE = 12.862%, MAE = 0.008, and R\({}^{2}\) = 0.810). In the next experiment, to better assess the predictive performance of the proposed ABC-LM-ANN, as well as the other benchmark models, a repetitive random subsampling consisting of 20 training and testing times was performed. In each run, 90% of the data is used for training the CC estimation model and 10% of the data is used as testing cases. The average computational time of the newly developed ABC-LM-ANN is 167.37(s); additionally, the proportions of computational time for global and local searching phases are 97.79% and 2.21%, respectively. The experimental results obtained from the repeated random subsampling process are reported in Table 4 with the mean and the standard deviation (Std) of the outcomes. This second experiment in this study points out that the average testing performance of the ABC-LM-ANN (RMSE = 0.010, MAPE = 12.586%, MAE = 0.007, and R\({}^{2}\) = 0.841) is better than those of the ANN models trained by LM and ABC, as well as the RegTree model. Moreover, the two-sample \(t\)-test [69] is employed in this section to better demonstrate the statistical significance of the models' performances differences in terms of R\({}^{2}\). The R\({}^{2}\) is selected in this statistical \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{3}{*}{**Phase**} & \multirow{3}{*}{**Performance**} & \multicolumn{8}{c}{**Prediction Models**} \\ \cline{3-10}  & & & **ABC-LM-ANN** & **LM-ANN** & **ABC-ANN** & **RegTree** \\ \cline{3-10}  & & **Mean** & **Std** & **Mean** & **Std** & **Mean** & **Std** & **Mean** & **Std** \\ \hline \multirow{2}{*}{Training} & RMSE & 0.008 & 0.000 & 0.009 & 0.001 & 0.011 & 0.000 & 0.005 & 0.000 \\  & MAPE (\%) & 10.981 & 0.453 & 11.585 & 1.246 & 15.059 & 1.053 & 5.949 & 0.332 \\  & MAE & 0.006 & 0.000 & 0.007 & 0.001 & 0.008 & 0.000 & 0.003 & 0.000 \\  & R\({}^{2}\) & 0.876 & 0.009 & 0.869 & 0.017 & 0.811 & 0.014 & 0.962 & 0.004 \\ \hline \multirow{2}{*}{Testing} & RMSE & 0.010 & 0.001 & 0.010 & 0.001 & 0.012 & 0.001 & 0.012 & 0.002 \\  & MAPE (\%) & 12.586 & 1.822 & 13.042 & 1.520 & 16.852 & 3.561 & 15.015 & 1.965 \\  & MAE & 0.007 & 0.001 & 0.008 & 0.001 & 0.009 & 0.001 & 0.009 & 0.001 \\  & R\({}^{2}\) & 0.841 & 0.039 & 0.817 & 0.046 & 0.788 & 0.057 & 0.744 & 0.060 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The result obtained from the repetitive random subsampling with 20 runs. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Phase**} & \multirow{2}{*}{**Performance**} & \multicolumn{4}{c}{**Prediction Models**} \\ \hline  & & **ABC-LM-ANN** & **LM-ANN** & **ABC-ANN** & **RegTree** \\ \hline Training & RMSE & 0.009 & 0.009 & 0.010 & 0.005 \\  & MAPE (\%) & 12.117 & 11.730 & 14.674 & 6.374 \\  & MAE & 0.007 & 0.007 & 0.008 & 0.004 \\  & R\({}^{2}\) & 0.860 & 0.873 & 0.821 & 0.955 \\ \hline Testing & RMSE & 0.009 & 0.010 & 0.010 & 0.010 \\  & MAPE (\%) & 10.705 & 12.400 & 14.029 & 12.862 \\  & MAE & 0.007 & 0.008 & 0.008 & 0.008 \\  & R\({}^{2}\) & 0.840 & 0.811 & 0.792 & 0.810 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Model result comparison. test due to its indication of how well the regression models have fitted the collected dataset. It is noted that the significant level (\(p\)-value) of the \(t\)-test is 0.05. The outcomes of the two-sample \(t\)-test are reported in Table 5. The results show that the proposed hybrid ABC-LM-ANN has achieved a win over the LM-ANN, as well as two significant wins over ABC-ANN and RegTree.