A dependent variable is regressed on K independent variables, using n sets of sample observations.

We denote SSE as the error sum of squares and R2 as the coefficient of determination for this estimated regression. We want to test the null hypothesis that K1 of these independent variables, taken together, do not linearly affect the dependent variable, given that the other 1K - K12 independent variables are also to be used. Suppose that the regression is reestimated with the K1 independent variables of interest excluded. Let SSE* denote the error sum of squares and R*2, the coefficient of determination for this regression. Show that the statistic for testing our null hypothesis, introduced in Section 12.5, can be expressed as follows:

1SSE* - SSE2>K1 SSE>1n - K - 12 =

R2 - R*2 1 - R2 #

n - K - 1 K1