Question

When using best subsets regression with a model that has four independent variables, a total of ________ different combinations of regression models will be considered.

a. 4
b. 15
c. 12
d. 18

Answer 1

b. 15

Explanation:

Given that:

There are 4 independent variables, then the subset regression total is 2⁴ = 16 attainable regression model.

However, out of these 16 regression models, 1 Model contains no predictors which only intercept 3 Model with
`(X_1), (X_2), (X_3)`, 3 Model with
`(X_1,X_2), (X_1,X_3), (X_2,X_3)`. and 1 Model which comprises all the independent variables.

Therefore, when applying best subsets regression with a model that possesses four (4) independent variables, the number of different combinations of regression models that can be considered is 15.