Question

A regression tree approach was used to describe the effect of 7 different covariates (x1 through x7) on monthly sales. The tree is shown below In each model, only the significant covariates are shown Branch: is x3.5? YES NO Model: Branch is x? 2.0? y 1200 +400x 500x3-8x R2-0.68 YES NO Model Model: y-500700x3-8x,7 R2-0.82 y-800+300x, 8x, R2-0.72 Questions 8a, 8b 0.0/8.0 points (ungraded) a. Select all of the following statements that are true according to this regression tree The effect ofr7 is the same regardless of the values of 2 1 and 2 o x1 is only important when its value is small (less than 3.5) x2 is irrelevant when predicting monthly sales x5 is irrelevant when predicting monthly sales O The regression tree can predict monthly sales better for values of ar1 above 3.5 than for values of 1 smaller than 3.5 b. A random forest model was built for the same purpose, using the same 7 covariates. Which of the following statements are true? O The random forest model contains many trees with different branchings O The random forest model uses many trees, but returns a single tree solution that can be analyzed O The random forest model can report the relative importance of each variable

Answer 1

a)

The effect of x7 is the same irrespective of the values of x1 and x2 as the coefficient of x7 is always -8 in all the regression equations in all cases.

X1 is only important when it’s value is less than 3.5 because only in that case the regression model has x1 as a significant variable.

X2 is not irrelevant in predicting the monthly sales as there are 2 different equations based on whether x2 has value greater than 2.

X5 is irrelevant in predicting monthly sales as it is not coming as a significant variable in regression models and it is not changing the course of the tree in any node.

The regression tree can predict monthly sales better for values above 3.5 than for values smaller than 3.5 as the R-squared values are higher (0.82,0.72) in the former as compared to the latter (0.68).

b)

The random forest model contains many trees with different branching and the final result would result from an ensemble of the outputs of different trees.

The random forest does not return a single tree, it simply predicts using a combination of outputs form different trees.

The random forest model can report the relative importance of each variable.