Methods and formulas for the model summary in CART^® Regression

Any regression tree is a collection of splits. Each split provides improvement to the tree. Each split also includes surrogate splits that also provide improvement to the tree. The importance of a variable is given by all of its improvements when the tree uses the variable to split a node or as a surrogate to split a node when another variable has a missing value. The following formula gives the improvement at a single node:

The values of I(t), p_Left, and p_Right depend on the criterion for splitting the nodes. For more information, go to Node splitting methods in CART® Regression.

The formula for the relative importance for the q^th predictor scales the importance by the most important variable:

R² is also known as the coefficient of determination.