5. Suppose a population regression equation is: Y_i=β₀ +β₁X_i +u_i. Y_i, X_i, and ui denote the dependent variable, independent variable, and the error term, respectively. i indexes cach individual observation. Which of the following statement is correct?
(A) Ifand the correlation between X_i and u_i is zero, the OLS estimator is unbiased.
(B) If and the correlation between X_i； and u_i； is zero, the OLS estimator  is inconsistent.
(C) , the correlation between Xi and ue may not be zero.
(D) The assumption that the correlation between X_i and u_i is zero cannot be tested empirically.
(E)None of the above choices (a)-(d). 

6.In Equation 2, holding all other factors constant, when Age increases by I year, what is the predicted change in Earnings? (A)Increase by 370 dollars. (B) Increase by 1448 dollars. (C) Increasc by 0.37%. (D) Increase by 37%. (E) None of the above choices (a)-(d).

7.Suppose Equation 2 is the correct model. That is, Age is a determinant of a person's carnings. Are older people more likely than younger people to have a college degree in this sample?(A) Older people are more likely to have a college degree. (B) Younger people are more likely to have a college degree.(C) All people are equally likely to have a college degree. (D) We don't have sufficient information to answer this question. (E) None of the above choices (a)-(d).

8. Which of the following is false? (A)If all Gauss-Markov conditions are satisfied, the OLS estimators have the lowest conditional variance among all linear conditionally unbiased estimators. (B) If not all Gauss-Markov conditions are satisfied, the OLS estimators are biased. (C) If the regression error ui is conditionally heteroscedastic, the OLS estimators can still be consistent. (D) If the conditional variance of ui is heteroscedastic and its functional form is known and can be estimated exactly, we may prefer a weighted least square estimator to an OLS estimator because of the efficiency consideration. (E) None of the above choices (a)-(d). 

9. Lot size (Lsize) is measured in square meters. If you change the unit of measurement to square centimeters. What will be the new estimated coefficient of Lsize? (A)(B)(C) 50 x 102 (D) 50 x 104 (E) None of the above choices(a)-(d).

10. H0: The coefficients of NBR and Age are jointly zero. Ha: The coefficient of NBR and Age are not jointly zero. You H0 using a F-test, with the test statistic = 2.2. Probability(F-statistic ＞ 2.2) = 0.03, Which of the following is correct? (A)You can reject H0 at the 10% level, but not at the 5% level. (B) You can reject H0 at both the 10% and 5% levels, but not at the 1% level. (C) You can reject H0 at the 10%, 5% level, and 1% levels. (D) You cannot reject H0 at the 10%, 5% level, or 1% level. (E) None of the above choices(a)-(d). 

1.Suppose X and Y have a bivariate normal distribution with covariance 1. X has a mean of 10 and standard deviation of 4. Y has a mean of 15 and standard deviation of 6. Z = 2X + 3Y. Which of the following statement is false? (A)The mean of Z, is 65. (B) The variance of Z is 400. (C) The correlation between X and Y is 1/24. (D) Z follows a normal distribution. (E) None of the above choices (a)-(d).

2. Y is distributed N(0,4), and X is distributed N(0,16). Please calculate E(Y2) and E(X3). (A)E(Y2) = 4 and E(X3) = 16 (B) E(Y2) = 2 and E(X3) = 64 (C) E(Y2) = 4 and E(X3) = 0 (D) E(Y2) = 2 and E(X3) = 8 (E) None of the above choices(a)-(d).

3. A random draw (with replacement) of 1000 balls from a pool of several million balls is conducted. Each ball is either blue or red. Let p denote the fraction of blue balls in the population. Let denote the fraction of blue balls in the sample. You want to test the competing hypotheses Ho: p = 0.4 vs. H1: p≠0.4. Suppose that you decide to reject. Note that the sample of 1000 balls is considered as a large sample. What is the type I etror of this test? (A)0.197 (B) 0.261 (C) 0.325 (D) 0.413 (E) 0.522

4.Suppose you estimate a sample OLS regression model using 20 observations (for i = 1,2, ..., 20). The resulted regression equation is: Yi = 2.11 + 3.58Xi +εi. Yi, Xi, and εi denote the dependent variable, independent variable, and the regression residual, respectively. If Xi is equal to 2 for i = 1,2 .... 4； equal to 3 fori = 5,6 ,..., 10； equal to 11 for i = 11, 12； equal to 14 for i =13, 14, ... 20, what is the value of Y? (A)30.75 (B) 28.96 (C) 26.12 (D) It cannot be determined. (E) None of the above choices (a)-(d).

Problem 20. The number of collisions at sea in a year is Poisson distributed. Thus, the length of time between collisions follows:(A) a Poisson distribution also.(B) a normal distribution.(C) an exponential distribution.(D) a Bernoulli distribution.(E) None of the above.

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