7.Suppose a population regression model is: Y_i =β₀ + B₁X_i + u_i. Y_i, X_i, and ui denote the dependent variable, independent variable, and the error term, respectively. i indexes each individual observation. are the OLS estimators, and is the regression residual, using a sample of n observations. Which of the following statement is false?
(A)
(B)
(C)Suppose and the correlation between X_i and u_i is zero. Then, the OLS estimator is inconsistent.
(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)

1. Firm size (Size) is measured in million dollars. If you change the unit of measurement to billion dollars. What will be the new estimated coefficient of Size? (A) (B) (C) 0.4 x 103 (D)0.4✖103 (E)None of the above choices (a)-(d).

2. Ho: The coefficient of BM is zero. Ha: The coefficient of BM is not zero. You test H0 using a t-test, with the test statistic = 2.36. Probability(t-statistic ＞ 2.36)-0.0091. Which of the following is correct? (A) You can reject H0 at the 10% level, but no ot at the 5% level. (B) You can reject H0 at both the 10% and 5% leve (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).

3. IfX1，X2, .... Xn are mutually independent normal random variables, with their means all equal to 3 and variances equal to 10, what is the variance of Y =?(A)400 (B) 200 (C) 400n (D) 200n (E) None of the above choices (a)-(d).

4. Y is distributed , and K is distributed . Suppose Probability(Y S 16) = 0.90. Please calculate Probability(K ≤ 1.6). (A) 0.09(B)0.45(C) 0.75 (D)0.90  (E) None of the above choices (a)-(d).

5. A random draw (with replacement) of 1000 balls from a pool of several million balls is conducted. Each ball is cither 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 H0: P = 0.4 vs. H1: P ≠0.4. Suppose that you decide to reject  Note that the sample of l 000 balls is considered as a large sample. What is the type I error of this test? (A)0.178 (B)0.256(C)0.367 (D) 0.488 (E) 0.519

6. Suppose you estimate a sample OLS regression model. The resulted regression equation is: Yi = 4.1 + 3.5 Xi +εi.Yi， Xi, and εi denote the dependent variable, independent variable, and the regression residual, respectively: indexes cach individual observation. If X, is equal to 2, what is the predicted value of Yi?(A)23.5 (B) 19.6 (C) 15.2 (D) 11.1 (E) None of the above choices (a)-(d).

8. In Equation 2, holding all other factors constant, when Total.Assets increases by 1%, what is the predicted change in Earnings? (A) Increase by 250 dollars. (B) Increase by 1284 dollars. (C)Increase by 0.25%. (D) Increase by 25%. (E) None of the above choices (a)-(d).

9. Suppose Equation 2 is the correct model. That is, a firm's total asset size is a determinant of an employce's earnings. Are larger firms (measured by total asset size) more likely than smaller firms to employ college graduates? (A) Larger firms are more likely to hire college graduates. (B)  Smaller firms are more likely to hire college graduates. (C) All sizes of firms are equally likely to hire college graduates. (D) We don't have sufficient information to answer this question. (E) None of the abo bove choices (a)-(d).

10. Which of the following is false? (A) If all Gauss-Markov conditions are satisfied, the OLS estimators are unbiased. (B) If all Gauss-Markov conditions are satisfied, the OLS estimators are consistent. (C) If all Gauss-Markov conditions are satisfied, the OLS estimators have the lowest conditional variance among all linear conditionally unbiased estimators. (D) Ifthe conditional variance of ui is heteroscedastic, then Gauss-Markov conditions are violated and the OLS estimators are biased. (E) None of the above choices (a)-(d).

複選題18. A survey with size of 150 was conducted to investigate whether gender (male versus female) is associated with annual salary (the dependent variable), after controlling for years of experience, years of education, and the position level categorized as "top or middle level manager', "first-line manager", and "non-manager". You want to conduct a multiple linear regression model. Which of the following is/are correct? (A) When testing for the overall significance of the model, the degree of freedom for the critical value of F is (6, 143)； (B) Assuming that we treat "male" as a reference group for the gender variable, the estimated coefficient is interpreted as the additional amount of women's annual salary compared with male's, after years of experiences, years of education, and the position level are held constant； (C) To test whether years of education is significant factor on annual salary after adjusting other variables, we can use t-test with a degree of freedom of 144 to detect whether its estimated coefficient is different from 0； (D) Given that the 95% confidence interval of the coefficient for years of experience is (500, 1000), its estimated coefficient is definitely a positive value； (E) The variable of "position level" has to be converted to a numerical variable by assigning "non-manager" as O, "first-line manager" as 1, and "top or middle level manager" as 2 in order to be included in the regression model.

110年 - 110 國立臺灣大學_碩士班招生考試_財務金融研究所甲、丙組:商用統計學#105747

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