## 5 Simulation Study
### Simulation Results
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & **Algorithm** & **MSE** & **RMSE** & **MAE** & **Selected Trees** \\ \hline Class 1 & Ntree = 100 & ECAPRAF–Lasso & 8.771454854 & 2.941930802 & 2.340062232 & 38 \\  & & ECAPRAF–EN & **8.755369012** & **2.939273653** & **2.338975803** & **49** \\  & & ECAPRAF–GL & 8.834635058 & 2.952447098 & 2.353491403 & 50 \\ \cline{2-6}  & & & & & \\ \cline{2-6}  & & & & & \\ \cline{2-6}  & & & & & \\ \cline{2-6}  & & & & & \\ \cline{2-6}  & & & & & \\ \hline \multirow{2}{*}{\begin{tabular}{c} Ntree = 240 \\ ECAPRAF–EN \\ ECAPRAF–GL \\ \end{tabular} } & ECAPRAF–Lasso & 8.48091468 & 2.896388688 & 2.311120159 & 48 \\  & & ECAPRAF–EN & **8.435537518** & **2.88973851** & **2.306854126** & **58** \\  & & ECAPRAF–GL & 8.460982026 & 2.893231877 & 2.309807383 & 85 \\ \cline{2-6}  & & & & & \\ \cline{2-6}  & & & & & \\ \cline{2-6}  & & & & & \\ \hline \multirow{2}{*}{\begin{tabular}{c} Ntree = 200 \\ ECAPRAF–EL \\ ECAPRAF–EL \\ ECAPRAF–EL \\ ECAPRAF–EL \\ \end{tabular} } & ECAPRAF–Lasso & 8.6025055 & 2.91579362 & 2.321329903 & 40 \\  & & ECAPRAF–EN & **8.569467143** & **2.911295916** & **2.313871952** & **54** \\  & & ECAPRAF–GL & 8.573476967 & 2.911484803 & 2.316801795 & 65 \\ \cline{2-6}  & & & & & \\ \cline{2-6}  & & & & & \\ \cline{2-6}  & & & & & \\ \hline \multirow{2}{*}{\begin{tabular}{c} Ntree = 300 \\ ECAPRAF–EN \\ ECAPRAF–EL \\ ECAPRAF–EL \\ ECAPRAF–EL \\ \end{tabular} } & ECAPRAF–Lasso & 8.570308727 & 2.907906984 & 2.315400928 & 49 \\  & & & **8.487885223** & **2.894469963** & **2.310524005** & **55** \\  & & ECAPRAF–GL & 8.543043047 & 2.902892836 & 2.313360543 & 60 \\ \hline \multirow{2}{*}{\begin{tabular}{c} Class 2 \\ ECAPRAF–EL \\ ECAPRAF–EL \\ ECAPRAF–EL \\ ECAPRAF–EL \\ \end{tabular} } & ECAPRAF–Lasso & 8.568160746 & 2.907691807 & 2.276576336 & 46 \\  & & & **8.537230028** & **2.902463664** & **2.271534304** & **50** \\  & & ECAPRAF–GL & 8.707072382 & 2.932313251 & 2.298910393 & 85 \\ \cline{2-6}  & & & & & \\ \hline \multirow{2}{*}{\begin{tabular}{c} Ntree = 260 \\ ECAPRAF–EL \\ ECAPRAF–EL \\ ECAPRAF–EL \\ ECAPRAF–EL \\ \end{tabular} } & ECAPRAF–Lasso & 8.646290595 & 2.919224788 & 2.275972475 & 35 \\ \cline{2-6}  & & & **8.625681531** & **2.915495283** & **2.270765139** & **48** \\  & & ECAPRAF–GL & 8.789112679 & 2.943872273 & 2.300908247 & 90 \\ \hline \multirow{2}{*}{\
\begin{tabular}{c} Ntree = 600 \\ ECAPRAF–EL \\ ECAPRAF–EL \\ ECAPRAF–EL \\ ECAPRAF–EL \\ \end{tabular} } & ECAPRAF–Lasso & 8.63919584 & 2.916575153 & 2.270767945 & 50 \\  & & & **8.588438862** & **2.907950701** & **2.264518857** & **59** \\  & & ECAPRAF–GL & 8.684550424 & 2.92488069 & 2.285283869 & 95 \\ \hline \multirow{2}{*}{
\begin{tabular}{c} Ntree = 700 \\ ECAPRAF–EL \\ ECAPRAF–EL \\ ECAPRAF–EL \\ ECAPRAF–EL \\ ECAPRAF–EL \\ \end{tabular} } & ECAPRAF–Lasso & 8.611153953 & 2.910771216 & 2.26987304 & 54 \\  & & **8.579999482** & **2.905078274** & **2.264884094** & **63** \\  & & ECAPRAF–GL & 8.652976321 & 2.919281462 & 2.281626936 & 105 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The results of the proposed method for the linear model in the clusters. Figure 6: Bar plot showing the difference among the 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.