Question

Exercise 1 Answer the following questions: a. Consider the multiple regression model y-Xe subject to a set of linear constraints of the form Cß-γ, where C is mx (k + 1) matrix. The Gauss-Markov conditions hold and also ε ~ N(0, σ21) Is it true that we can test the hypothesis C9-γ using a k¿SSRfillm d SKreducedmodel Please explain b. Refer to question (a). Let H and Hi be the hat matrices of the full and reduced model respectively. Show that H- Hi is an idempotent matrix. c. Refer to question (a). Suppose C-(0,0, 0,0,1), and γ-0. Describe each part of the following formula and explain why this is the relevant test. What is the distribution of this test statistic? d. Consider the sc gX h h ic hypothesis are we testing here? What is the distribution of istic M) , which this test statistic under the hypothesis? What is the distribution of this test statistic if the hypothesis is not true. Please provide all the details

Answer 1

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