Multiple choice: (3 points each) Identify the letter of the choice that best completes the statement or answers the question. Use the following information to answer the next two questions. You have collected 14,925 observations from the Current Population Survey. There are 6,285 females in the sample, and 8,640 males. The females report a mean of average hourly earnings of $16.50 with a standard deviation of $9.06. The males have an average of $20.09 and a standard deviation of $10.85. The overall mean average hourly earnings is $18.58. 1. Using the t-statistic for testing differences between two means, decide whether or not there is sufficient evidence to reject the null hypothesis that females and males have identical average hourly earnings (use alpha=.01). (a) Reject the null hypothesis (b) Do not reject the null hypothesis (c) Not enough evidence to either reject or accept the null hypothesis (d) None of the above 2. You decide to run two regressions: first, you simply regress average hourly earnings on an intercept only: Average hourly earnings = Bo + u. Next, you repeat this regression, but only for the 6,285 females in the sample. What will the regression coefficients be in each of the two regressions? (a) $3.59, $20.09 (b) $18.58, $20.09 (c) $3.59, 16.50 (d) $18.58, $16.50 3. For Y, = Bo+ RX, + 1, test Ho: B1 = 1 vs. Hi: Bi > 1 if the following regression information are given: b = 1.39, $, =0.18, and n = 30. (a) Reject Ho for a = 0.01 (b) Reject H for a = 0.05 (c) Reject Ho for a = 0.005 (d) None of the above 4. Imagine you regressed earnings of individuals on a constant, a binary variable ("Male") which takes on the value 1 for males and is 0 otherwise, and another binary variable ("Female") which takes on the value 1 for females and is 0 otherwise. Because females typically earn less than males, you would expect (a) the coefficient for Male to have a positive sign, and for Female a negative sign. (b) both coefficients to be the same distance from the constant, one above and the other below. (c) none of the OLS estimators to exist because there is perfect multicollinearity. (d) this to yield a difference in means statistic. Page 2 of 9F. In multiple regression, the R" increases whenever a regressor is a. added unless the coefficient on the added regressor is exactly zero. b. added. c. added unless there is heteroskedasticity. d. greater than 1.96 in absolute value. Use the following information to answer the next two questions. The STATA regression output below shows the relationship between the market return (sp500_return) and the return of the Microsoft company's stock (msft_return) regress moft_return sp500_return Source df MS Number of obs 11 8, 091 F (1, 8089) 2560 . 24 Model 1. 25129567 1. 25139567 Prob > F 0. 0000 Residual 4.26969294 8,089 . 000527839 R-squared Adj R-squared 0. 2403 Total | 5.62108861 8, 090 . 000694819 Root MBE . 02297 moft_return Coel Sed. Err. 1950 Conf. Interval] up500_return 1 . 145417 . 0226372 0. 000 1 . 101043 1 . 189792 cons 0001438 . 0002555 0.56 0. 574 - 0003572 0006447 6. In the regression model moft_return, = Bo + 81sp500_return, + u, what is the proportion of the variability of the return of the Microsoft company' stock explained by the variability in S&P returns? a. 0.240 b. 0.310 c. 0.760 d. 0.440 7. In the regression model meft_return, = Bo + Bisp500_return, + u, what is the value of the statistic for testing the following hypothesis: HO: 1 =1 vs. H1 : B1 #1 ? a. 20.22 b. 50.60 c. 6.42 d. 10.15 8. In the estimated regression model Test Score = 607.3 + 3.85 Income - 0.0423 Income , the following income level results in the maximum test score a. 607.3. b. 91.02. C. 45.50. d. cannot be determined without a plot of the data. Page 3 of 99. In the assumptions of the linear regression model, which of the following is not one of the assumptions regarding the error term? (a) The mean of the error term is 0. (b) The error term follows the t-distribution. (c) The variance of the error term is constant. (d) The error terms across observations are independent of one another. Use the following information to answer the next question. Using relevant data, we estimate the following regression in STATA: Inflation, = Bo + B Unemployemnt, + ByInflation,-1 + up regress inflation unemployment L. inflation Source df Number of obs = 191 2, 168] = 224 .52 Model 1202 .36741 2 Prob > F = 0. 0000 Residual 188 R-squared = 0.7049 Adj R-squared = 0. 7017 Total | 1705.76941 190 Root MSE inflation Coel. Err. t PaltI 1950 Conf. Interval] unemployment -. 1068234 .0847486 -1.26 0. 209 - . 2740039 060357 inflation L1 . .8493857 . 0405491 20.95 0 . 000 . 769396 .9293754 cons 1. 234229 . 5073066 2. 43 0 . 016 - 2334844 2 . 234974 10. What is the value of Root Mean Squared Error (or Root MSE)? a. 503.40 b. 1202.37 C. 2.68 d. 1.63