Question

When using the cart algorithm, the gini index is used in the classification tree, however in a regression tree, ________ is used to measure impurity?

1) Mean Squared Error
2) Entropy
3) Information Gain
4) Variance

Answer 1

In a regression tree of the CART algorithm, Variance is used to measure impurity rather than the Gini index, which is suitable for classification trees. Option 4 is correct.

Step-by-step explanation:

When using the CART (Classification And Regression Tree) algorithm, the Gini index is used to measure impurity in a classification tree. However, in a regression tree, Variance is used to measure impurity. The Gini index is useful for categorical target variables, representing the probability of a randomly chosen sample being incorrectly labeled if it was randomly labeled according to the distribution of labels in the dataset.

In contrast, for regression trees where the target variable is continuous, the Variance measures how much the numerical data is spread out, which is analogous to the use of Mean Squared Error (MSE). A low variance indicates that the data points tend to be close to the mean and to each other, implying a more homogenous node.