Answer the following questions: 3.. Consider the simple regression model yi 2 lm,- + 66, 3' = 1, ..., n. The Gauss-Markov conditions hold and also Eu; N N (0, a). Test the hypothesis Ho : ,81 : 3 against the alternative Hr '. ,81 y 0.4 using the t statistic. Refer to question (a). Test the hypothesis Hg : ,81 = 0.4 against the alternative H a : ,6'1 y 3 using the F statistic. Refer to question (a). Test the hypothesis Ho : 51 = 0.4 against the alternative If.1 : [31 i 3 using the likelihood ratio test. Show that it is equivalent to the F statistic. Refer to question (a). Test the hypothesis Ho : ,81 = 0.4 against the alternative H'.1 : {'31 3 using the extra sum of squares method (full and reduced models). Apply the test statistics you constructed in (a), (b), (c), and (d) using the following data set in R