Question: 5. Using the Supervisor Performance data, test the hypothesis Ho : B1 = $3 = 0.5 in each of the following models : (a) Y

5. Using the Supervisor Performance data, test the hypothesis Ho : B1 = $3 = 0.5 in each of the following models : (a) Y = Bot B1X1+ B3X3 + 8 (b) Y = Bot BIX1 + B2X2 + B3X3 + = Table2. Supervisor Performance Data Row Y X X2 X3 X4 X5 X6 W 6. Consider the two models : RM : Ho : Y = = FM : H1 : Y = Bo + B1X1 + ... + BpXp+ & (a) Develop an F-test for testing the above hypotheses. (b) Let p = 1 (simple regression) and construct a data set Y and X, such that Ho is not rejected at the 5% significance level. (c) What does the null hypothesis indicate in this case? (d) Compute the appropriate value of RZ that relates the above two models. 7. Read Appendix in pages 82-84 of our textbook. Show that B and 82 are independent. * Bonus question We assume that Y~MVN(XB, 21) where I is a n x n identity matrix. Show that zeTe~x2(df = n - p - 1) where e = Y - Y (hint: look at the supplementary material: quadratic form)

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