Question: Suppose that a dependent variable is related to K independent variables through a multiple regression model. Let R2 denote the coefficient of determination and R2,

Suppose that a dependent variable is related to K independent variables through a multiple regression model. Let R2 denote the coefficient of determination and R2, the corrected coefficient. Suppose that n sets of observations are used to fit the regression.
a. Show that

b. Show that

c. Show that the statistic for testing the null hypothesis that all the regression coefficients are 0 can be written as

where
A = K / n €“ K €“ 1

K1 SSR/K -K 1 R2 A SSE/( K 1) 1- R

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