## 7 Discussions  
In this paper, the ECAPRAF model is proposed to increase the RF algorithm accuracy and reduce the computational time. In the proposed model, the k-means clustering algorithm clusters the data. RF extracts the prediction trees. The shrinkage methods such as lasso, elastic net, and group lasso are used to reduce the number of random-forest trees. The generated trees are input into lasso, group lasso, and EN algorithms for tree reduction. Finally, the remaining trees are ensembled.  
Our combined model achieved a higher accuracy in comparison to published study [6] that used only lasso to reduce the number of RF trees. In the present proposed model, after clustering the simulation result of the linear model with 500 trees, the MSE in our proposed  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Algorithm** & **WMSE** & **WRMSE** & **WMAE** & **Selected Trees** \\ \hline \multirow{2}{*}{Ntree = 300} & Random Forest & 12.05356086 & 3.471823852 & 2.192973908 & 300 \\  & ECAPRAF–Lasso & 11.2855362 & 3.359395213 & 2.262931613 & 84 \\  & ECAPRAF–EN & **10.55174201** & **3.248344504** & **2.157154185** & **106** \\  & ECAPRAF–GL & 11.57883518 & 3.402768752 & 2.226525129 & 105 \\ \hline \multirow{2}{*}{Ntree = 500} & Random Forest & 11.85795023 & 3.443537459 & 2.190326265 & 500 \\  & ECAPRAF–Lasso & 10.93821866 & 3.307297788 & 2.234521671 & 92 \\  & ECAPRAF–EN & **10.38014764** & **3.221823651** & **2.140801457** & **128** \\  & ECAPRAF-GL & 10.5635914 & 3.245975837 & 2.151589584 & 100 \\ \hline \multirow{2}{*}{Ntree = 800} & Random Forest & 11.88962813 & 3.448134007 & 2.125427866 & 800 \\  & ECAPRAF–Lasso & 11.41440075 & 3.378520497 & 2.277955818 & 100 \\  & ECAPRAF–EN & **9.588927134** & **3.096599285** & **2.07692437** & **129** \\  & ECAPRAF–GL & 10.97505102 & 3.312861454 & 2.231254518 & 105 \\ \hline \multirow{2}{*}{Ntree = 1000} & Random Forest & 11.73102545 & 3.425058459 & 2.116374462 & 1000 \\  & ECAPRAF–Lasso & 8.927716935 & 2.987928536 & 2.041401696 & 100 \\  & ECAPRAF–EN & **8.67016921** & **2.944515106** & **2.021913684** & **128** \\  & ECAPRAF–GL & 9.407644139 & 3.067188312 & 2.055927983 & 140 \\ \hline \hline \end{tabular}
\end{table}
Table 6: The results of the proposed method for the Boston house-price dataset.  
Figure 8: Bar plot of the difference in proposed methods based on 500 trees. The RMSE value of ECAPRAF–EN is the lowest value among the three algorithms. Elastic net also has the highest reduction compared to other shrinkage methods.  
model reached 8.56 compared to 21.64 in [6]. In the real datasets, i.e., Boston house price and real-estate valuation, the MSE reached 10.93 and 32.94 in our model, respectively, compared to 12.84 and 61.97 in [6]. Moreover, we used the elastic-net method instead of lasso, which resulted in the better performance of EN than lasso.  
Using the RF trees as the input of the EN method to reduce the number of trees, ECAPRAF-EN achieved a 12% error reduction, which was the highest reduction compared to other methods. It means that the proposed model has much higher accuracy and smaller error compared with the traditional methods, which proves that the proposed model is effective and has better performance.  
Although ECAPRAF-EN improved the accuracy of prediction compared with other methods, we will choose deep-learning methods and different ensemble methods to further study in future work in order to improve the model performance and prediction accuracy.