Solved – Explanatory power of a Decision Tree

Question

With Multiple Regression, the R-Squared gives the researcher an estimate of the explanatory power of the regression equation.

What is the equivalent for Decision Trees?

Answer 1

Decision tree usually "overfit" the data (in the sense that every point is assigned to a specific class) if you don't provide them early stopping criterion when you grow the tree. However, you can use out-of-bags estimate to get a pseudo R squared.

Per example, for a regression random forest, R offers an implementation of the pseudo R squared.

Value
An object of class randomForest, which is a list with the following components:
[...]
rsq (regression only) “pseudo R-squared”: 1 - mse / Var(y)