You are given the multiple regression model y=B0+ 1x1 + B2x2 + B3x3 + u, where...

   

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You are given the multiple regression model y=B0+ 1x1 + B2x2 + B3x3 + u, where u is an unobserved error term and you have a sample of size n. You are interested in testing the null hypothesis against the alternative Ho B2 =0 and 3 = 0 H B20 or B3 0. (i) [8 marks] Can you test this hypothesis with a t test, or do you need some other test? Explain briefly. (ii) [7 marks] Suppose instead that you wish to test the null hypothesis against the alternative Ho: B = 0 H: B2 < 0. Propose a test for this null and alternative hypothesis, writing down the formula of the test statistic along with its distribution under Ho. You are given the multiple regression model y=B0+ 1x1 + B2x2 + B3x3 + u, where u is an unobserved error term and you have a sample of size n. You are interested in testing the null hypothesis against the alternative Ho B2 =0 and 3 = 0 H B20 or B3 0. (i) [8 marks] Can you test this hypothesis with a t test, or do you need some other test? Explain briefly. (ii) [7 marks] Suppose instead that you wish to test the null hypothesis against the alternative Ho: B = 0 H: B2 < 0. Propose a test for this null and alternative hypothesis, writing down the formula of the test statistic along with its distribution under Ho.