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Microsoft Word - Mid sem test 2 solution.docx 1 Intermediate Econometrics Mid semester Test 2 Thursday 13 September 2018 Please answer all questions in the answer sheet provided. All questions are worth 2 points for a total 30 points. This test is worth 15% of your final grade for Intermediate Econometrics. Use the following information to answer questions 1-2. Suppose that you are collecting data from a survey of households for an empirical analysis. Further assume that one of the questions asks for the annual income of the household and the answer choices are: (1) $0 - $50,000; (2) $50,001 - $75,000; (3) $75,001 - $100,000; (4) $100,001 - $125,000; (5) $125,000 and higher. 1. Refer to the information above. Suppose that the probabilities of selecting a household in each income bracket is: ; ; ; ; . This list of probabilities is an example of _____. a. random variable b. random experiment c. probability density function d. cumulative distribution function 2. Refer to the information above. Suppose that the probability of choosing a household with an annual income of $100,000 or less is 75%. That is, . This is an example of a _____. a. random variable b. random experiment c. probability density function d. cumulative distribution function Use the following information to answer question 3 Suppose you have collected demographic information about households in your local area. The following table is the joint probability density function for the number of children under the age of 18 living in the household and the marriage status of the adult taking the survey. Marriage Status/# of Children 0 1 2 3 4+ Single 0.20 0.10 0.05 0.04 0.01 Married 0.1 0.3 0.25 0.03 0.02 ( )( )1 0.20P X = = ( )( )2 0.40P X = = ( )( )3 0.15P X = = ( )( )4 0.15P X = = ( )( )5 0.10P X = = ( )100,000 0.75P X £ = 2 3. Using the information above, the expected value of the number of children in the household is _____ (treat the 4+ category as 4). a. 1.3 b. 2.0 c. 2.5 d. 3.3 4. Suppose you have the following estimated regression equation: . What would the predicted value be when the independent variable is 15.00? a. 196.76 b. 16.30 c. 244.50 d. 32.19 5. Suppose you have estimated a simple linear demand equation for single-game tickets for a minor league baseball team. The estimated equation is where is the number of tickets sold measured in thousands and is the dollar price of a ticket. Further assume that the point of the means is . Given this information and everything else held constant, the estimate of the price elasticity of demand for tickets is _____. a. -0.16 b. 1.64 c. 0.16 d. -1.64 6. Suppose using the data obtained from 1000 Australian households, you estimate a regression model of weekly consumption expenditure of milk (M) on weekly household income (Y) as follows. [Note: the variables are measured in Australian dollars.] ?" = 25 + 0.064? Which of the following statements is true? a. If income increases by $1, households’ expenditure on milk consumption will decrease by 64 cents. b. If income is $0, households’ expenditure on milk consumption is also approximately $0. c. If income increases by $100, households’ expenditure on milk consumption increases by $64. d. If income decreases by $1000, households’ expenditure on milk consumption decreases by $64. 7. A model estimated using a dataset with 65 observations generates the following results. Variable ?- Std. Error t P>|t| x2 -0.01264 0.005519 -2.28937 0.022 3.41 12.89y x= +! 4.58 0.51q p= -! q p ( ) ( ), 10.25,3.19p q = 3 x3 0.595792 0.014482 41.13934 0.000 x4 1.124589 0.877192 1.282032 0.200 x5 0.323742 0.060709 5.332661 0.000 Constant 8.86016 1.766116 5.016749 0.000 What are the endpoints for the 99% confidence interval for b5? a. (0.1673, 0.4852) b. (-5.0089, 5.6564) c. (0.2630, 0.3845) d. (0.1786, 0.4688) 8. If you are performing a left-tailed significance test and find the area to the left of |tc| is .99, what is the p-value? a. 0.01 b. 0.99 c. 0.02 d. 0.05 9. Suppose you estimate a simple regression model and you obtain ?/0 = 156.25 and SSR=6250. What is your sample size? a. 42 b. 40 c. 44 d. 48 10. You estimate a simple linear regression model using a sample of 62 observations and obtain the following results (estimated standard errors in parentheses below coefficient estimates): y = 97.25 + 33.74* x (3.86) (9.42) You want to test the following hypothesis: H0: b2 = 12, H1: b2 ≠12. If you choose to reject the null hypothesis based on these results, the probability you have committed a Type I error is _____. a. between .05 and .10 b. between .01 and .025 c. between .02 and .05 d. impossible to determine without knowing the true value of b2 4 11. You have estimated a regression model and your printout includes the following information: sxy= 3614.00 sx = 12.72 sy = 394.61 SST = 758912.00 Where Sxy is the sample covariance between x and y Sx is the standard deviation of x Sy is the standard deviation of y SST is the total sum of squares. What is R2 for this regression model? a. 0.72 b. 0.11 c. 0.03 d. 0.52 12. You have estimated the following simple regression model: y = 379 + 1.44 x3 What is the elasticity when x = 8.49? a. 263.19 b. 311.39 c. 2.10 d. -24.7 13. While working with the sales manager of your firm you have estimated the following model of sales volume as a function of monthly household income: (0.781) (0.392) Where Q is monthly sales volume, ln(I) is the log of monthly household income in thousands, and standard errors are listed below the parameter estimates. What is the income elasticity of your firm’s product? a. 1.212 b. 2.206 c. 3.418 d. 4.630 )ln(*212.1418.3)ln( IQ += 5 Use the following information to answer questions 14-15. Variable ?- Std. Error t P>|t| x2 -0.01264 0.005519 -2.28937 0.022 x3 0.595792 0.014482 41.13934 0.000 x4 1.124589 0.877192 1.282032 0.200 x5 0.323742 0.060709 5.332661 0.000 Constant 8.86016 1.766116 5.016749 0.000 14. What test statistic would you use to test the hypothesis ?3≥0.25? a. 1.2147 b. 5.3327 c. 1.2948 d. 0.0607 15. If you want to test the hypothesis ?3 = 0.47. What p-value does this test statistic generate if you are performing a two-tailed test? a. 0.000 b. ≃between0.02 and 0.01 c. ≃between 0.05 and 0.1 d. 0.05 End of test Statistical tables to follow 6 Statistical Tables