## 2 Materials and Methods
### Methods
#### 2.3.3 Machine Learning Models  
1. CART  
The classification and regression tree (CART) is a predictive tree model for investigating data structure. It creates visualized decision rules for predicting a categorical and continuous variable. The regression tree does not generate classes of dependent variables, unlike the classification tree (which splits the input space of many variables into subspaces, each subspace associated with a specific class of output variable). However, in the matrix of the independent variables, dependent variables represent the response values for each observation. Because regression trees do not contain preassigned classes, the stage's output is a response value for each of the new dependent variable observations. The squared residuals minimization procedure is used to make the splitting rule in regression trees, which indicates that the predicted sum variances for two resulting nodes should be minimized. The classification and regression tree, proposed by [PERSON] et al. [31], is one of the most widely used approaches for dealing with classification and regression issues. CART models execute the Gini and the least-squared deviation measurements for categorical and numerical issues, respectively [32]. Let the \(p\)th sample be illustrated as \(\big{(}I_{p,1},I_{p,2},\ldots\ldots I_{p,n}\ldots O_{p}\big{)}\), where \(I_{p,n}\) is the value of the \(p\)th sample with \(n\) features, and \(O_{p}\) is the corresponding output value of the sample. The minimization of the least-squared deviation measure of impurity given by Equation (1) serves as a choice to decide the split-up of trees into branches for a CART regression issue. \[\frac{1}{N}\sum_{V\in U_{r}}\big{(}O_{p}-\overline{O}_{r}\big{)}^{2}+\frac{1} {N}\sum_{V\in U_{l}}\big{(}O_{p}-\overline{O}_{l}\big{)}^{2} \tag{1}\]  
\(U_{r}\) and \(U_{l}\) are training data sets pointing to the right and left child nodes, respectively, and Nis the total number of training samples. The output values of the right and left nodes are represented by \(\overline{O}\) and \(\overline{\overline{O}}_{l}\) respectively. 2. Random Forest  
The random forest classifier comprises many tree classifiers, each of which is created using a random vector sampled separately from the input vector, each of which casts a unit vote for the most popular class to categorize an input vector [33]. The random forest classifier employed in this work grows a tree by randomly selecting or combining features at each node. For each feature/feature combination selected, bagging, a method for generating a training dataset by randomly drawing with replacement N instances, where N is the size of the original training set, was employed. Any instances are categorized by selecting the class with the highest votes from all the tree predictors in the forest (Breiman). The decision tree design process necessitated the selection of an attribute selection measure and a pruning technique. There are several ways to select characteristics for decision tree induction, and most approaches explicitly give a quality measure to the attribute. The information gain ratio criteria and the Gini index are the most often utilized attribute selection metrics in decision tree induction. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**A**} & \multicolumn{1}{c}{**B**} & \multicolumn{1}{c}{**C**} & \multicolumn{1}{c}{**D**} & \multicolumn{1}{c}{**E**} & \multicolumn{1}{c}{**F**} & \multicolumn{1}{c}{**G**} & \multicolumn{1}{c}{**H**} & \multicolumn{1}{c}{**I**} & \multicolumn{1}{c}{**J**} \\ \hline  & **0-** & **15,001–** & **18,001–** & **20,001–** & **25,001–** & **32,001–** & **40,001–** & **45,001–** & **50,000–** & **80,001–** \\  & **15,000** & **18,000** & **20,000** & **25,000** & **32,000** & **40,000** & **45,000** & **50,000** & **80,000** & **130,000** \\ \hline Training & 833 & 529 & 2166 & 2409 & 2253 & 16,084 & 1416 & 584 & 2686 & 2566 \\ SMOTE & 3153 & 3153 & 3153 & 3152 & 3152 & 3153 & 3152 & 3153 & 3153 & 3152 \\ \hline \hline \end{tabular}
\end{table}