Consider the multiple regression model Yi = ẞ1 + ẞ2xi1 + ... .... + ẞkxik + Ei where the Ę;'s are independent and identically distributed as N(0, 02) for i = 1, . . ., n, and k is the number of parameters. 1. Show that an equivalent form of the usual F-test for testing the significance of the regression can be based on R2 (squared multiple correlation coefficient) as follows: To test Hoẞ2 = ẞ3 = = ßk = 0 versus H1: at least one ß; ‡ 0, calculate =...= R2 (n-k) Fo - (k − 1)(1 − R2) and reject Ho if the computed value of Fo exceeds Fa a,k,n-k. 2. Suppose a linear regression model as in part (1) with two regressors has been fitted to n = 25 observations and that R2 = 0.90. Test for the significance of the regression at a = 0.05.

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