## 6 The Real Data Analysis  
The performance of the random-forest, ECAPRAF-Lasso, ECAPRAF-EN, and ECAPRAF-GL algorithms are described through two real datasets. The utilized datasets contain Boston house prices and real-estate valuations. The basic information of the two datasets is shown in Table 4. The Boston house-price dataset contains 506 observations and 13 variables whose response variable is the median of the owner-occupied house price. The data were first published by [PERSON] and [PERSON] [37] and are publicly available through the MASS package in R ([[https://cran.r-project.org/package=MASS](https://cran.r-project.org/package=MASS)]([https://cran.r-project.org/package=MASS](https://cran.r-project.org/package=MASS)) (accessed on 7 May 2021)). Another dataset includes real-estate valuations from the UCI machine-learning repository (accessed on 7 May 2021). The original owners of this dataset are [PERSON] and [PERSON] [38], and it consists of seven variables from which five variables are selected including house age, distance to the nearest MRT station, number of convenience stores in the living circle on foot, latitude, longitude, the transaction date, and the house price of the select unit area as the independent variable and the house price of the unit area as the dependent variable. In the simulation section, the datasets are first clustered, then in each cluster, 80% of the data are selected for the training set, and the remaining datasets are selected for the testing set. In this study, glmnet, gglasso, NbClust, and randomForest packages in R are used. In the real-estate valuation and Boston house-price datasets, the data are divided into three and two clusters in which different trees are used in each cluster, respectively. In the RF algorithm, Ntree = 300, 500, 800, and 1000 are considered for the total number of trees of clusters and different trees in each cluster. The 3D scatter plot is drawn in Figure 7, which shows the number of clusters and the scattering of points in three dimensions. Each cluster is shown in a various color. As can be seen in Figure 7a, two clusters are obtained for the Boston house-price dataset, highlighted in blue and red. The first red-colored cluster contains 369 samples, and the other blue-colored cluster contains 137 samples. The dataset consists of 13 features from which 3 features, namely, the average number of rooms (rm), the pupil-teacher ratio by town (ptratio), and the weighted distances of employment centers (dis) are used to draw the diagram. For the real-estate-valuation dataset: three clusters colored blue, red, and green are identified including 41 samples in the first cluster, 93 in the second cluster, and 280 in the third cluster. The diagram is shown in Figure 7b. The predicted results of the proposed technique (ECAPRAF) are shown for the real-estate-valuation dataset in Table 5 and the Boston house-price in Table 6. The WMSE, WRMSE, and WMAE are calculated for different trees. The WRMSE, WMAE, and WMSE, obtained for RF, are based on the Boston house-price dataset, 3.4435, 2.1903, and 11.8579, respectively. In contrast, the values obtained with the proposed technique for ECAPRAF-EN are 3.2218, 2.1515, and 10.3801, respectively. As can be seen, the proposed method has a 12% reduction compared to RF. There is also a significant reduction in real-estate valuation, the results are shown in Table 5. In these datasets, the ECAPRAF presents more acceptable results than the traditional RF. Additionally, ECAPRAF-EN yields more efficient results than other shrinkage methods. Additionally, not only does the ECAPRAF-EN select many trees compared to ECAPRAF-Lasso, but it also has a lower WMSE, WRMSE, WMAE, and a great performance. Other algorithms have a better performance than RF. Therefore, it is concluded that the ECAPRAF-EN algorithm improves the performance of RF by reducing the number of trees and also outperforms other algorithms. The performance of the proposed technique and RF in terms of WRMSE is indicated in Figure 8.