Hi

i need help with my Multivariate statistical analysis quest

Question 4. [17 marks] Consider the following multiple regression model: where e, iid N(0, a ) and i = 1, ..., n. (1) [5 marks] Suppose we wish to test the hypothesis Ho: , = $2 = 3. Clearly explain how to perform this test using "full" and "reduced" models where "full" model means when He is not true and "reduced" model when Ho is true. Your answer should include the test statistics, its distribution and the decision rule for this hypothesis. (2) [6 marks] Now suppose we wish to test H: , = 1 and ; = 0. Explain how to perform this test WITHOUT using the Full and Reduced models. (3) [6 marks] Explain how to construct Bonferroni simultaneous 100(1 - a)% Cl for contrasts 82 - 83 and 61 - B3.Question 4. [17 marks] Consider the following multiple regression model: where e, iid N(0, o ) and i = 1, ..., 7. (1) [5 marks] Suppose we wish to test the hypothesis Ho: $, = $2 = $3- CI perform this test using "full" and "reduced" models where "full" model true and "reduced" model when H, is true. Your answer should include distribution and the decision rule for this hypothesis.Question 4. [17 marks] Consider the following multiple regression model: Vi = Bo+ PIXji + Paxzi + ByXai + Ex where 6, lid N(0, o') and / = 1, ..., n. (1) Suppose we wish to test the hypothesis Ho: /2 = /3. Clearly explain how to perform this test. Your answer should include the test statistics, its distribution and the decision rule for this hypothesis. (3) Explain how to construct a 100(1 - a)% Cl for #2 - By. (2) Now suppose we wish to test /o: 2 = 0 and ; = 0. Explain how to perform this test using the Full and Reduced model approach