Buec 333 Summer 1997 D. Maki FINAL EXAMINATION - A Important - record on the top front of your answer sheet the letter "A", "B" or "C" from the examination title above. This examination consists of 30 multiple choice questions. Choose the letter corresponding to the one best answer to each question. Your grade will be computed on the basis of the number of correct answers. The exams will be machine graded, and making the answers legible to the machine is your responsibility. Use soft pencil (HB or softer) only. Fill in the appropriate circles corresponding to your name on the back of the answer sheet. This is a "closed book" examination - no books or notes are allowed. A formula sheet and tables are attached. Total time allowed = 3 hours. 1. For a simple regression problem involving 7 observations, assume Y = 3, 4, 4, 6, 5.5, 5.5, 7 and X = 1, 2, 3, 4, 5, 6, 7 (observations for X and Y are in the same order). The slope coefficient, b, for the estimated linear regression of Y on X is then: a. 0.12 b. 1.12 c. 0.33 d. 1.33 e. none of the above PROBLEMS 2 and 3 REFER TO THE FOLLOWING PROBLEM SETTING. A time series of 9 years of annual data on the U.K. yielded the following information on disposable income, X, and saving, Y: Variable X Variable Y Mean 20.133 1.2789 Total SS 89.616 2.22168 Variance 11.202 0.27771 Std. Dev. 3.347 0.52698 The correlation between X and Y, r, is 0.95555. 2. Regressing Y on X, the coefficients are: a. a = -17.959, b = 0.956 b. a = -17.103, b = 0.913 c. a = -1.750, b = 0.150 d. a = 12.371, b = 6.069 e. impossible to calculate from the information given. 3. Testing the two-tailed hypothesis that the population correlation coefficient is zero at the alpha = .05 level, the appropriate conclusion is: a. accept Ho: since 0.96 < 1.895 b. accept Ho: since 0.96 < 2.365 c. reject Ho: since 8.58 > 1.895 d. reject Ho: since 8.58 > 2.365 e. reject Ho: since 11.99 > 2.365 4. Given the following 24 observations on a time series variable which is to be tested for randomness: 67, 63, 58, 62, 55, 56, 50, 57, 55, 43, 47, 23, 31, 38, 49, 33, 43, 34, 42, 51, 66, 54, 55, 49 The number of runs is: a. 5 b. 6 c. 7 d. 8 e. none of the above 5. Given a simple regression model Y = a + bX + e, if one calculates: aäY + bäXY - (1/n)(äy)2, this yields: a. the sum of squares due to regression, SSR b. the slope coefficient, b c. the standard error of estimate, S2 d. the slope coefficient in the regression of X on Y e. the squared correlation coefficient, r2 6. Assume we have a regression model, Y = a + bX + e, relating data on fuel economy for 30 automobiles (Y) to the size of the engine (X). It is given that: ä(X - þ)2 = 1000 the standard error of estimate, Se, = 1.00 the mean of X, þ, = 250 Then, for one individual automobile with an engine of size 250 inches3, the width of the 95% confidence interval for the fuel economy is: a. 0.75 b. 2.05 c. 4.16 d. 4.23 e. not calculable from the information given 7. A Value index (or total cost index), if multiplied times 100, is equal to: a. Fisher's ideal price index x Laspeyres quantity index b. Fisher's ideal price index x Paasche price index c. Laspeyres price index x Laspeyres quantity index d. Paasche price index x Laspeyres quantity index e. none of the above 8. In a multiple regression involving two independent variables, Y = a + b1X1 + b2X2 + e, it is determined that SST = 1000 and SSE = 100. If n = 30, then the calculated test statistic for testing Ho: á1 = á2 = 0 is: a. 1.5 b. 3.1 c. 121.5 d. 252.0 e. not calculable from the information given 9. Given the following data on a price index: Year 1980 Base 1990 Base 1985 101.0 1986 95.9 1987 117.3 1988 129.5 1989 131.4 1990 140.0 100.0 1991 95.7 The 1991 value in a spliced index with a 1980 base is: a. 68.4 b. 95.7 c. 134.0 d. 195.7 e. 235.7 QUESTIONS 10 AND 11 REFER TO THE FOLLOWING PROBLEM SETTING. In a marketing test, 8 people were asked to rate two brands of cola on a scale of 0 (worst) to 10 (best). The results are shown below: Person Cola "C" Rating Cola "P" Rating 1 9.0 7.0 2 10.0 9.5 3 7.5 6.0 4 8.0 8.0 5 6.0 6.5 6 7.0 9.0 7 8.5 10.0 8 4.0 4.5 10. What is the value of the rank correlation coefficient between the two ratings? a. 0.44 b. 0.67 c. 0.97 d. 0.99 e. can't be calculated because of ties 11. Assuming that you test whether the correlation is zero at the .05 level using the result from question 10, the best interpretation is: a. overall, people prefer cola "C" b. overall, people prefer cola "P" c. overall, people have no preference between brands d. some people like "C", others like "P" e. some people like cola more than other people do 12. Autocorrelated errors in regression models: a. causes the estimated slope coefficients to be biased b. make the usual variance estimators wrong c. is a problem of the sample, not the population d. is a problem only if it is first order autocorrelation e. all of the above 13. Assume a snack food basket consists of only three goods, popcorn, potato chips and pretzels. Given the following information on prices and quantities, a Paasche price index for 1995 using 1990 as the base year has the value: Item Price 1990 Price 1995 Quantity 1990 Quantity 1995 Popcorn $2.20 $3.00 50 40 Potato Chips $2.00 $2.00 2 3 Pretzels $ .50 $ .60 80 100 a. 92.1 b. 93.5 c. 129.2 d. 131.2 e. 135.0 14. Using quarterly data on local government employment, if the modified means of the ratio-to-trend values are: Q1 = 92.4, Q2 = 104.3, Q3 = 101.2, Q4 = 104.3, the value of the Final Seasonal Index for the first quarter is: a. 92.4 b. 92.9 c. 91.4 d. 91.9 e. greater than 100 15. In a simple regression model, Y = a + bX + e, it is estimated by least squares that b = 2.6. Further, it is given that ä(Y - ý)2 = 45 and ä(Y - ý)(X - þ) = 17. Then the estimated standard error of b is: a. 0.012 b. 0.12 c. 1.20 d. 12.00 e. not calculable from the information given. 16. If you regress Y = a1 + b1X1 + v and X1 = a2 + b2X2 + u, the simple correlation between v and u is: a. zero b. the partial correlation of Y and X1 b. the partial correlation of Y and X2 c. the partial correlation of X1 and X2 d. unity 17. The Gauss-Markov theorem is important because it: a. is a justification for the use of least squares b. reinforces the Central Limit Theorem c. provides formulas for the estimated variances d. holds for Normal populations even if the estimators are biased e. holds for large samples even if the estimators are biased QUESTIONS 18 AND 19 REFER TO THE FOLLOWING PROBLEM SETTING. A sociologist wishes to test the null hypothesis that at least 20% of Catholics are favourable to the idea of ordaining women as priests, against a one-tailed alternative. Using a sample of size n=100, she decides to reject Ho if 15 people or less are favourable to the idea. 18. What is à, the probability of Type I error? a. just under 5 percent b. between 5 and 10 percent c. just over 10 percent d. greater than 50 percent e. not calculable from the information given 19. What is á, the probability of Type II error, if the true p=.10? a. about 95 percent b. about 92 percent c. about 89 percent d. about 50 percent e. less than 20 percent 20. Assume for a multiple regression equation: Y = a + b1X1 + b2X2 + e it is known that the simple correlation between Y and X1 = 0, the simple correlation between Y and X2 is positive and the simple correlation between X1 and X2 = 0. If one estimates the indicated multiple regression from these data, the coefficient of X1 will be: a. zero b. positive c. negative d. positive, negative or zero, it is impossible to tell e. positive or zero, but not negative 21. Annual sales for a grocery store are recorded for a six-year period as shown below: Year Sales ($Millions) 1 5 2 4 3 9 4 11 5 10 6 13 A prediction of sales in year 7 using an exponential smoothing model with alpha = 0.3 is (rounded to an integer): a. 11 b. 12 c. 13 d. 14 e. 15 22. Given the following data: X = -2 -1 0 1 2 Y = 2 1 1 0 1 If one estimates a nonlinear relationship based on a quadratic equation in X, the resulting equation is: a. Y = 0.5 + 0.3 X + 0.2 X2 + e b. Y = 0.5 + 0.3 X - 0.2 X2 + e c. Y = 0.5 - 0.3 X - 0.2 X2 + e d. Y = 0.5 - 0.3 X + 0.2 X2 + e e. not estimable - X and X2 are perfectly correlated 23. Suppose a regression model using 140 observations of monthly data was estimated as Y = a + bX + e with R2 = .63. Assume the model was re-estimated as Y = a + bX + b2D2 + b3D3 + ... + b12D12 + e, with R2 = .89, where D2, D3, ... D12 are eleven dummy variables equal to unity for the second, third , ... and 12th months of the year, respectively, and zero otherwise. Testing whether the data exhibited a seasonal pattern yields the calculated test statistic: a. 14.4 b. 27.3 c. 36.2 d. 75.1 e. 79.2 24. For a simple regression model: Y = a + bX + e, estimated using time series data, which of the following is the least likely application to satisfy the assumptions of the Classical Linear Regression Model? a. for a province, Y = gasoline consumption, X = number of vehicles licensed b. for a corporation, Y = dividends paid, X = earnings per share c. for a country, Y = Federal government tax revenue, X = gross domestic product d. for a city, Y = air pollution index, X = average outside temperature e. for an industry, Y = sales, X = profits 25. With two variables, Y and X, if one regresses Y on X, i.e. Y = a + bX + e; and also regresses X on Y, i.e. X = a* + b*Y + e*, then we know that in general: a. b = b* b. b = 1/b* c. the standard error of b = the standard error of b* d. a will equal 1/a* e. none of the above 26. The investment firm of Dewey, Cheatham and Howe suspects that the amount of money invested with their firm differs for the first half of the week (Monday through noon Wednesday) versus the second half of the week (Wednesday noon through Friday). Data for eight weeks follows: Week 1 2 3 4 5 6 7 8 First half 70 69 63 73 68 71 72 71 Second half 67 64 66 68 62 69 72 77 Testing the implied two-tailed hypothesis, the calculated test statistic is: a. 0.94 b. 1.33 c. 2.33 d. 2.65 e. 3.00 27. For a given value of X, the confidence interval for the prediction value from a simple regression equation will be just as wide whether the prediction is viewed as the mean of Y for that given X or an individual value of Y for that given X: _ a. if the given X = X b. if the given X = 0 c. if n is very large d. if the confidence level is very high e. never 28. A random sample of n=500 persons living in a metropolitan area is suveyed to determine whether they prefer a morning or afternoon newspaper, and whether they live in the city or in a suburb. To test whether newspaper preference is independent of city versus suburban home, one should use: a. a Chi-square test b. a Z-test for equality of proportions c. a correlation test d. either the test in part a or part b will work e. the tests in parts a, b and c will all work 29. A number of people hold more than one job, with the job they work at for the most hours per week known as the primary job and all others known as secondary jobs. A study using micro data on several hundred multiple job holders published the following equation: WS=37.07+0.403*WP-90.06*R+75.51*URB+47.33*HS+113.64*D+2.26*A (0.062) (24.47) (21.60) (23.42) (27.62) (0.94) where: WS = wage in secondary job(s) WP = wage in primary job R = a dummy equal to unity for nonwhites URB = a dummy equal to unity for urban dwellers HS = a dummy equal to unity for high school graduates D = a dummy for persons living in the West A = age in years and standard errors for coefficients are shown in parentheses. Which of the following is most likely a true statement, based on the above results? a. secondary jobs pay less than primary jobs b. older workers are more likely to be multiple job holders c. urban workers are more likely to be multiple job holders d. nonwhites are more likely to be multiple job holders e. urban workers in the west are more likely to be multiple jobholders than other urban workers 30. Consider a multiple regression model with two independent variables, i.e. Y = a + b1X1 + b2X2 + e, estimated using time series data with the variable Y displaying a strong positive time trend. If the following are the scatterplots of each of the independent variables against Y, without doing any calculations we can say: X1 X2 9| 9|x x 8| x 8| 7| x 7| x 6| x x 6| x x 5| x x 5| x x 4| x 4| x 3| 3| x 2|x x 2| 1|_______________ Y 1|________________ Y a. the R2 should be at least 0.95 b. multicollinearity will be a serious problem c. autocorrelation will be a serious problem d. will be a serious problem e. none of the above