la. Show that the F-statistic for testing a single restriction, i.e., when J = 1, is...

 

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la. Show that the F-statistic for testing a single restriction, i.e., when J = 1, is equal to the square of the t-statistic for testing the same hypothesis. b. Suppose you have the regressions [A] [B] Y₁ = Bo + B₁X₁,i+... BK-1XK-1,i+€, Y₁ = Bo + B₁X₁,i+... 3K-1XK-1,i+BKXKi + €₁. (9.20) Two possible ways of deciding whether or not to include variable XK in the regression is to do a t-test (or an F-test) of the hypothesis K = 0. Another way is to see whether or not the Adjusted-R2 in [B] is greater than the Adjusted-R2 in [A]. Show that the latter method is equivalent to including XK; if the absolute value of the t-statistic for 3 in [B] is greater than 1. la. Show that the F-statistic for testing a single restriction, i.e., when J = 1, is equal to the square of the t-statistic for testing the same hypothesis. b. Suppose you have the regressions [A] [B] Y₁ = Bo + B₁X₁,i+... BK-1XK-1,i+€, Y₁ = Bo + B₁X₁,i+... 3K-1XK-1,i+BKXKi + €₁. (9.20) Two possible ways of deciding whether or not to include variable XK in the regression is to do a t-test (or an F-test) of the hypothesis K = 0. Another way is to see whether or not the Adjusted-R2 in [B] is greater than the Adjusted-R2 in [A]. Show that the latter method is equivalent to including XK; if the absolute value of the t-statistic for 3 in [B] is greater than 1.

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