Multiple linear regression model is used to predict annual i

Multiple linear regression model is used to predict annual income (Y) using number of years of education (X₁) and number of years employed in current job (X₂) using a 5% level of significance. Regarding coefficient of determination:

a.

It is possible that coefficient of determination is equal to 0.30 in a simple linear regression model using only X₁, and equal to 0.26 in a multiple linear regression using both X₁ and X₂.   

or

b.

It is impossible that coefficient of determination is equal to 0.30 in a simple linear regression model using only X₁, and equal to 0.26 in a multiple linear regression using both X₁ and X₂.

Solution

a) may take place when X2 is a factor whihc does not affect y.