Society of Actuaries PA Practice Exam Study Guide

A decision tree is constructed through a process of recursively partitioning the data based on the predictor variables. This method involves evaluating the potential splits in the data that lead to the most significant increase in predictive power, often assessed using measures such as information gain or Gini impurity. As various splits are considered, the decision tree branches into distinct regions that correspond to different outcomes of the response variable.

This technique allows the model to capture nonlinear relationships between the predictors and the response variable, as well as interactions among predictors. Each split creates a node in the tree, and the process continues until a stopping criterion is met, such as a maximum tree depth or a minimum number of samples per leaf.

The random selection of predictor variables, fitting a single linear model to the entire dataset, or averaging response values in distinct regions does not align with the methodology of decision tree construction. These other methods do not effectively capture the hierarchical and recursive nature of decision trees or account for complex relationships within the data.