The null hypothesis for the test for the model (Section 8.3) does not include the intercept term β 0 . Give the interpretation of a null hypothesis that did include β 0 , H 0 :β 0 = β 1 = ... = β m =...

The null hypothesis for the test for the model (Section 8.3) does not include the intercept term β₀. Give the interpretation of a null hypothesis that did include β
₀, H₀:β₀
= β₁
= ... = β_m
= 0. Explain why this hypothesis would rarely be of interest.

In a data set with 12 observations, you try fitting two regression models. The estimated models are summarized as:

Model 1: Y^ 5 3:5 + 2x; SSR = 20; SSE = 10;

Model 2: Y^ = 3:0 + 1:5x + 0:4x²; SSR = 23; SSE = 7:

(a) Calculate R²
for both models.

(b) For both models, test the null hypothesis that all the regression coefficients (other than the intercept) are 0.

(c) Test the null hypothesis that Model 2 is not better than Model 1.