Theorem 8.1d. If y is N,(XB. o'D). the distribution of F = SSR/(ko?) SSR/K SSE/[(1 - k - 1)o?] SSE/(n - k - 1) (8.5) is as follows: (i) If Ho: B, = 0 is false, then F is distributed as F(k, n - k - 1, A; ). where Al = BIX'X.B, /202. (ii) If Ho: B, = 0 is true, then A = 0 and F is distributed as F(k, n - k - 1). Theorem 8.3. The F statistics in (8.5) and (8.17) for testing Ho : B =0 and Ho : B, = 0, respectively, can be written in terms of R- as F = (B'X'y - ny)/ k (vy - BX'y)/(n - k - 1) (8.22) R- / k = (1 - R2)/(n - k - 1) (8.23)If B; # 0, we can subtract B, in (8.40) so that t; = (B; - B;)/s gj has the central distribution, where go is the jth diagonal element of (X'X) . Then P -ta/2.0-K-15 B; - Bi