"NO" need to check for multicollinearity or remove correlated variables explicitly when using decision trees.

Multicollinearity is a phenomenon in which two or more independent variables in a regression model are highly correlated. This can cause issues when interpreting the model and can affect the stability and reliability of the coefficients estimated by the model. Multicollinearity doesn't impact decision trees in the same way it affects linear regression models, but it's still important to understand the distinction between the two and why multicollinearity might not be a concern for decision trees.

Understanding Multicollinearity in Linear Regression:

In linear regression, the goal is to estimate the relationship between the independent variables and the dependent variable. When independent variables are correlated, it becomes difficult to isolate their individual effects on the dependent variable. For example, consider a dataset trying to predict a student's performance based on two features: hours studied and hours slept. If these two features are highly correlated (which is likely the case since students who study more tend to sleep less), the model might find it challenging to differentiate between the effects of studying and sleeping on performance.

Decision Trees and Multicollinearity:

Decision trees, on the other hand, are a non-linear modeling technique. They recursively split the data based on the features to create subsets, making decisions at each node. Decision trees are inherently capable of capturing complex relationships between variables, including nonlinear ones.

Here's why multicollinearity isn't a significant concern for decision trees:

1. Variable Selection: Decision trees perform feature selection implicitly during the training process. At each node, the algorithm chooses the feature that best splits the data, making decisions based on the available features. It doesn't rely on coefficients like linear regression, so the presence of correlated features doesn't impact the model's ability to make decisions.
2. Splitting Criteria: Decision trees use metrics like Gini impurity or information gain to decide how to split the data. These metrics consider each feature individually without being influenced by the presence of other features. Even if two features are highly correlated, the tree can still choose the one that provides the best information gain for the split.

Example:

Let's take an example where we're trying to predict whether a person will buy a car (BuyCar) based on two features: monthly income (Income) and monthly expenses (Expenses). If Income and Expenses are highly correlated, it might be challenging for a linear regression model to estimate their individual effects accurately. However, a decision tree can handle this situation well.

Suppose the decision tree determines that Income is the best feature for the first split. It might find further splits based on Expenses in other branches, effectively capturing the combined effect of both variables without being confused by their correlation.

In summary, while multicollinearity is a concern for linear regression models, decision trees can handle correlated features effectively due to their inherent nature of recursive splitting and feature selection. Therefore, there's generally no need to check for multicollinearity or remove correlated variables explicitly when using decision trees.