Ex. 16.3

Ex. 16.3

Show that fitting a linear regression model using rules 1, 4, 5 and 6 in equation (16.14) gives the same fit as the regression tree corresponding to this tree. Show the same is true for classification, if a logistic regression model is fit.

Soln. 16.3

The claims follow by noting that rule 1, 4, 5 and 6 consist of the leaves of the tree. Recall discussions on regression tree (see, e.g., (9.10) - (9.14) in the text), fitting a regression tree reduces to fitting a linear regression once the leaves are finalized. As for classification, recall that logistic regression has the linear fit in its numerator and the same denominator for all classes, it's essentially the same as fitting a linear regression in this case.