We have used a sample of 30 observations to fit a regression model. The full model has nine regressors, the variance once estimate is 2 = MSE = 100, and R2 = 0.92.
(a) Calculate the F-statistic for testing significance of regression. Using = 0.05, what would you conclude?
(b) Suppose that we fit another model using only four of the original regressors and that the error sum of squares for this new model is 2200. Find the estimate of σ2 for this new reduced model. Would you conclude that the reduced model is superior to the old one? Why?
(c) Find the value of Cp for the reduced model in part (b). Would you conclude that the reduced model is better than the old model?