1. By using examples from the relevant statistical tables, explain the relationship between the t- and the F-distributions. For questions 2-5, assume that the econometric model is of the form V, = Bi + B2xz + Box3, + BexAr + Boxs, + 1, 14.531 2. Which of the following hypotheses about the coefficients can be tested using a t-test? Which of them can be rested using an F-test? In each case, state the number of restrictions. (a) Ho : B3 = 2 (b) Ho : B3 + 84 = 1 (C) Ho : By + 84 = 1 and B; = 1 (d) Ho : 8, = 0and B, = 0and B, = 0and 8: = 0 (e) Ho : B.8. = 1 3. Which of the above null hypotheses constitutes THE' regression F-statistic in the context of (4.53)? Why is this null hypothesis always of interest.... Appendix 4.2 177 whatever the regression relationship under study? What exactly would constitute the alternative hypothesis in this case? Which would you expect to be bigger - the unrestricted residual sum of squares or the restricted residual sum of squares, and why? 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 rest. What is your conclusion