(15 points) Assume that the econometric model is of the form y_t = ?1 + ?2 x_2t + ?3 x_3t + ?4 x_4t + ?5 x_5t + u_t. Which of the following hypotheses about the coefficients can be tested using a t-test? Which of them can be tested using an F-test? Please explain why. In each case, please also state the number of restrictions. a. H0: ?3 = 2 b. H0: ?3 + ?4 = 1 c. H0: ?3 + ?4 = 1 and ?5 = 1 d. H0: ?2 = 0 and ?3 = 0 and ?4 = 0 and ?5 = 0 e. H0: ?2?3 = 1 (20 points) You decide to investigate the relationship given in the null hypothesis of question 2, part (c). What would constitute the restricted regression? The regressions are carried out on a sample of 96 quarterly observations, and the residual sums of squares for the restricted and unrestricted regressions are 102.87 and 91.41, respectively. Perform the test at 1% significance level and 5% significance level. What is your conclusion?
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Identify which hypotheses can be tested using a t-test and which can be tested using an F-test. a. $H_0: B_3 = 2$ can be tested using a t-test because it involves only one restriction on a single coefficient. b. $H_0: B_3 + B_4 = 1$ can be tested using a t-test Show more…
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