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### UNFORMATTED ATTACHMENT PREVIEW

EC252 AUTUMN MID-TERM PRACTICE TEST, 2021 1. Answer each of the following questions based on the estimated relations given in each case: (a) [6 marks] What is the predicted change in y given a 2 unit change in x? ŷ = 3.2 − 6.4 x (b) [6 marks] What is the predicted change in y given a 1 percent change in x? ŷ = −9.1 + 81.2 log(x) (c) [6 marks] What is the predicted percentage change in y given a 1 unit change in x? \ = −3.6 + 0.022 x log(y) (d) [7 marks] What is the predicted percentage change in y given a 5 percent change in x? \ = 0.22 − 2.1 log(x) log(y) 2. You are given the multiple regression model y = β0 + β1 x1 + β2 x2 + β3 x3 + β4 x4 + u, (1) where u is an unobserved error term. (a) [5 marks] Classify the following as observable or unobservable: y, x1 , x4 , β0 , β3 , x3 . (b) [5 marks] Is the following statement true of false? “Adding another variable to the right hand side of (1) can never increase the explanatory power of the model.” Explain your answer briefly. (c) You are interested in testing the null hypothesis H0 : β1 = 3 against the alternative H1 : β1 > 3. (i) [3 marks] What is the name of the test you would use to test this hypothesis? (ii) [5 marks] Give the formula of the test statistic, for a sample of size n. (iii) [7 marks] Define all components of the test statistic in part (ii) above. 3. (a) Answer the questions below (i) [5 marks] Suppose that Y is distributed as t432 . Find P (Y ≤ 1.96). (ii) [5 marks] If W is an estimator of some parameter θ, is it generally true that M SE(W ) = var(W )? If not, then when is it true? (b) Consider the general multiple regression model y = β0 + β1 x1 + β2 x2 + . . . + βk xk + u, (2) where u is an unobserved error term. Suppose that var(u|x1 , x2 , . . . , xk ) = σ 2 . (i) [5 marks] Name one method for obtaining estimates of the βi , i = 0, . . . , k. No explanations necessary. (ii) [10 marks] You are given the following two estimates for σ 2 : s21 = SSR SSR and s22 = , n n−k−1 where n denotes sample size and SSR denotes the sum of squared residuals. Which one provides an unbiased estimate of σ 2 ? Explain briefly. 4. (a) [6 marks] State the Classical Linear Model (CLM) assumptions. Remember, there are six of them and we called them MLR.1 through MLR.6. (b) You are investigating the effects of smoking on stamina (measured by the variable stam) for a sample of sports-persons who are all smokers. You find the following ordinary least squares (OLS) regression resul