Show that the Type I anova for XXXXXXXXXXand XXXXXXXXXXare different. Provide an interpretation of each of the tests. Show that the Type II anova is the same for the two models. Which of the Type II...

Show that the Type I anova for (6.22) and (6.23) are different. Provide an interpretation of each of the tests.

Show that the Type II anova is the same for the two models. Which of the Type II tests are equivalent to Type I tests?

Show that the overall F-test for multiple regression with an intercept can be written as

where R₂
is the proportion of variability explained by the regression. Thus, the F-statistic is just a transformation of R₂.