You have fit a regression model with two regressors to a data set that has 20 observations. The total sum of squares is 1000 and the model sum of squares is 750.

(a) What is the value of R² for this model?

(b) What is the adjusted R² for this model?

(c) What is the value of the F-statistic for testing the significance of regression? What conclusions would you draw about this model if α = 0.05? What if α = 0.01?

(d) Suppose that you add a third regressor to the model and as a result, the model sum of squares is now 785. Does it seem to you that adding this factor has improved the model?