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Econometrics Practice Exam (10 multiple Choice Questions) I. Choose ONE answer only: _______#1. Which of the following is TRUE? a. Y~N(1,2) means that E[Y] = 3 b. Y~N(1,2) means that (Y 1) / 2 ~N(1,0) c. Y ~N(1,2) and Z~N(2,1) means that Y+Z~N(3,3) always d. Y ~N(1,2) and Z = Y + 3 means that Y + Z~N(5,2) e. Y ~N(1,2) and Z~N(2,1) and independent means that Y - Z~N(-1,3) ________#2. Suppose that f ( x) b for 0 < x < a. What values of a and b will ensure that f(x) is a pdf? a. a = 1/2 and b = 1 b. a = 1 and b = 1/2 d. b < 0 and a > 0 _______#3. Suppose that Y = AX + B. a. A2 b. A2 + B2 _______#4. a. c. a = 2 and b = 1/2 e. b = -1 and a = -1 Then var(Y) = ____? c. A2var(X) d. A2var(X) + B e. A2var(X) + B2 Which of the following is TRUE? (x t c. x ) 2 x 2 2 Nx 2 (x t x ) 2 x 2 Nx b. (x t d. x ) 2 x 2 N 2 x 2 (x t x) 0 _______#5. Suppose that Yt X t t and assume that we do NOT estimate with OLS. Instead we estimate by ̂ a. E[ ˆ ] ≠ Y X t . Therefore we know that t b. var( ˆ ) = 2N ( X t ) 2 _______#6. Suppose that Yt o 1 X t t . c. ˆ t Additionally, let our data be X1 = 2, X2 = 1, X3 = 0 and Y1 = 2, Y2 = 3, and Y3 = 1. The for o and 1 are therefore equal to ˆ1 a. ̂ 0 = 3/2 b. ̂ 0 =1 c. ̂ 0 = 2/3 and ˆ1 = 1/2 d. ̂ 0 = 3/2 and ˆ1 = 1/2 e. ̂ 0 = 2/3 and ˆ1 = -1 ________#7. and ˆ1 OLS estimates = 1 = -1 In the regression in problem #6 above, the estimate of 2 = _____. a. 3/2 _______#8. and 0 b. 1 c. 1/2 d. 1/4 e. 1/ 2 If Yt o 1 X t t , then for OLS, Yˆt ˆo ˆ1 X t ˆt . a. true b. false _______#9. Suppose that Yt X t t . X2 = 1, X3 = 0 and Additionally, let our data be X1 = 2, Y1 = 2, Y2 = 3, and Y3 = 1. The OLS estimates for is therefore equal to a. ˆ = 1/2 b. ˆ = 5/3 c. ˆ = 8/5 d. ˆ = 7/5 e. ˆ = 11/3 _______#10. Based on your calculations in #9 above, the estimate of 2 = _____. a. 23/4 b. 1 c. 21/10 d. 17/4 e. 1/ 2