Suppose that you are investigating the relationship between the dependent variable Y and two potential explanatory variables, X₁and X₂.We will compare the R²value for the multiple regression model with both X variables included (Model 1:Y = b₀+ b₁X₁+b₂X₂) to the two separate simple regression models built using X₁(Model 2:Y = b_0'+ b_1'X₁)and X₂(Model 3:Y = b_0''+ b_1''X₂) separately.

(a) Is it possible for the R²for Model 1 to be lower than those of Model 2 and Model 3?Explain why or why not.

(b) Is it possible for the R²for Model 1 to be larger than thesumof R²values from Models 2 and 3?Explain why or why not.