Multiple linear regression model is used to predict annual income (Y) using numb

Question

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:

Select one:

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.   

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.

Explanation / Answer

The correct option is (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.    

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