Question

(ModelA) Price = b0 + b1(House) + b2(#Bedrooms) + b3(Living_Area) + e

(ModelB) Price = b0 + b1(House) + b2(Living_Area) + e

Which model (A or B) has a higher R Square? If model A has a higher Adjusted R Square than model B does, which model do you prefer?

Answer 1

For Model A, we have 3 predictors whereas Model B has only two. Since R2 increases with the increase in number of predictors, Model A has higher value of R2.

The adjusted R-square value increases only if the new predictor improves the model more than is expected by chance. Here Model A has a new predictor #Bedrooms compared to Model B and has higher adjusted R-squared value. Thus the new predictor improves the model and hence we prefer Model A again.