BUEC 333 Summer 2000 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, with a value of 5 points each, for a total of 150 points on the examination. 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 answer sheet. This is a closed book examination - no notes are allowed. A formula sheet and tables are attached. Total time allowed = 3 hours. Infinite populations are assumed in all questions where population size is relevant. Note: the notation X**2 means X-squared. 1. The pairs of values given below are for X, a company's advertising expense (hundreds of dollars) and Y, the amount of the company's sales (thousands of dollars): X 2 4 6 8 10 Y 3 1 7 5 9 Find a and b for the regression equation Y = a + bX. a. a=0.20, b=0.80 b. a=0.04, b=0.83 c. a=2.00, b=0.80 d. a=1.86, b=0.83 e. none of the above 2. Given seven observations of data on Y, the rate of return of an investor's portfolio of stocks and X, the value of a stock exchange index during the same period, it is calculated that: Sum[(X-XBAR)(Y-YBAR)]=112, Sum[(X-XBAR)**2]=28 and Sum[(Y-YBAR)**2]=464. Hence the standard error of estimate, Se**2, for a simple linear regression model is: a. 448 b. 16 c. 3.2 d. 2.3 e. impossible to calculate from the information given 3. An example of testing where a one-tailed test might be more appropriate than a two-tailed test is: a. a random sample of bolts from a production line has a mean length of 35 mm, and we test whether these might have come from a population with a true mean of 30mm. b. we test a manufacturer's claim that 95% of the people who use her lipstick will not have an allergic reaction. c. a random sample of 100 electric light bulbs has a mean of 1000 burning hours and sigma of 20, and we test whether these might have come from a population with mean 975 and standard deviation 18. d. all of the above e. none of the above 4. In testing a two-tailed hypothesis about a single mean, if XBAR = 100, Sigma=16 and n=10, the critical value for alpha=0.01 is: a. 1.31 b. 1.64 c. 1.96 d. 2.58 e. 3.27 5. The correlation between two variables, Y and X, differs from the correlation between X and Y in that: a. one represents a causal relationship, the other does not b. one is the negative of the other c. one is unity minus the other d. one is the reciprocal of the other e. none of the above 6. If one estimates a multiple regression of Y=number of rooms in the house on X1=monthly hydro bill and X2=monthly phone bill, for some sample of homes, the result is: a. a standard multiple regression application b. a good example of multicollinearity c. likely heteroscedasticity d. probably non-significance for the coefficient of X2 e. silly 7. A berry farm produces strawberries and raspberries. The amounts produced and prices received for two years are given below. This year Last year Quantity Price Quantity Price Strawberries 1200 3.00 2200 4.00 Raspberries 800 4.20 1800 6.00 A Laspeyres index of prices this year using last year as the base is: a. 138.5 b. 72.2 c. 70.8 d. 49.0 e. 40.0 8. The specific problem introduced by the presence of multicollinearity in the data set manifests itself through: a. inflated standard deviations of estimated coefficients b. deflated t-values for the estimated coefficients c. failure to detect significant relationships between Y and some of the X's d. all of the above e. only a and b above 9. When testing for independence in a 2X2 contingency table using a Chi-square test, this is equivalent to: a. a binomial situation b. testing for a difference between two population proportions c. a z-test d. all of the above e. none of the above 10. In classical time series analysis, a moving average is assumed to capture: a. the trend component b. the cyclical component c. the seasonal component d. all of the above e. only a and b above 11. A graduating student goes back over their transcript and calculates a correlation coefficient of 0.95 between Y=grade in a course and X=number of pages in the required textbook for that course. This implies that: a. long textbooks cause good grades b. good grades cause long textbooks c. there is a positive association between grade and length of textbook d. the student works harder in courses with long textbooks e. both a and b 12. One of the best ways to determine whether some of the basic assumptions in the Classical Linear Regression model have been violated is to look at: a. a plot of the residuals b. the R-square c. the t-values for the coefficients d. the size of the SSE e. the F-value from ANOVA 13. You want to sell your house, and you decide to obtain an appraisal on it. Looking at past data you discover that actual prices obtained for houses and the appraisal given for them prior to their sale was as follows: Actual Price Appraisal Up to $200,000 $200,000 or more Up to $200,000 25 5 $200,000 or more 10 10 Based on these data we can say: a. the appraisal and the actual pprice are independent at a 5 percent significance level b. the appraisal and the actual price are independent at any significance level smaller than 50 percent c. the appraisal and the actual price are independent at a 1 percent significance level d. the appraisal and the actual price are dependent at a 1 percent significance level, thus the appraisal is worthwhile e. both a and b above are correct 14. In a time series regression model with 20 observations and 4 independent variables, the calculated Durbin-Watson statistic is 2.50. In a two-tailed test for the presence of autocorrelation conducted at the .05 level, the conclusion is: a. the test is inconclusive b. there is no evidence of autocorrelation c. there is evidence of autocorrelation d. heteroscedasticity must be making the test invalid e. none of the above 15. Given the following 6 observations of data, a two-tailed test of whether Spearman's rank correlation is zero conducted at the 0.10 level: Y: 1 2 3 4 6 7 X: 5 4 2 -1 0 1 a. cannot be conducted because of the negative observation b. leads to acceptance of the null hypothesis c. leads to rejection of the null hypothesis d. leads to an ambiguous result due to the small sample e. none of the above 16. In a multiple regression application using ten years of monthly time series data, 48 runs are observed in the signs of the residuals. Performing a two-tailed test for autocorrelation using a 0.05 significance level the appropriate conclusion is: a. the test is inconclusive b. there is no evidence of autocorrelation c. there is evidence of autocorrelation d. heteroscedasticity must be making the test invalid e. none of the above 17. Given two variables, X and Y, if we estimate simple regression equations: Y=a+bX+e and X=c+dY+v using ordinary least squares, where a, b, c and d are parameters and e and v are error terms, we know: a. b and d will have opposite signs b. d will equal 1/b c. if b is greater than 1, d will be less than 1 d. b+d must be less than 2 e. none of the above 18. Assume we test a null hypothesis: mean >= 100 against a one-tailed alternative: mean < 100, where n=25 and sigma is known = 10, and the test is conducted at the alpha=.10 level. If the true mean is 98, what is beta (the probability of type II error)? a. 0.90 b. 0.61 c. 0.50 d. 0.39 e. zero 19. The interest rate paid in Bank A and in Bank B in a sample of various months is given by: Bank A: 5, 5.5, 6 Bank B: 4, 8 Using Mann-Whitney to test whether the mean interest rates differ between banks, the U statistic: a. depends on which sample you call the first one b. cannot be calculated for samples this small c. equals 2 d. equals 3 e. none of the above 20. In a multiple regression with two explanatory variables, we estimate a, b1 and b2 using least squares. Using a sample of size n, we have the following information: b1*Sum(X1)=10, b2*Sum(X2)=10, Sum(Y)=100, a=4 Then the sample size, n, is equal to: a. 17.5 b. 170 c. 120 d. 80 e. 20 21. Regressing income (Y) in thousands of dollars per year on education (X1) in years and age (X2) in years for 5 people, we use the following 5 observations: Y X1 X2 50 10 40 55 15 40 61 11 50 59 9 50 70 10 60 Then in the equation Y=a+b1*X1+b2*X2+e we find: a. e = 0 for all observations b. a = 0, b1 = b2 =1 c. Sum(e**2)=0, b1=10, b2=1 d. both a and b are correct e. both b and c are correct 22. Eight people rate two cars (a Ford and a Honda) on a scale from 1-10. The differences in their ratings (rating for Ford minus rating for Honda) are: -2, -5, 1, 1, -6, -3, 0, -4 The calculated test statistic, T, for the Wilcoxon test: a. cannot be computed - there is a tie b. depends on whether we are doing a one or two-tailed test c. equals 2 d. equals 3 e. none of the above 23. A sample of 100 observations was taken, and the simple regression: Y=a+bX+e was estimated. The standard error of estimate, Se = 2.3, a = 0, b=1 and XBAR=10. The 95 percent confidence interval for E(Yp), where Yp is the prediction value of Y for X=XBAR, is: a. 10 +/- 0.23*t(.025)(98 df) b. 10 +/- 0.23*t(.025)(100 df) c. 10 +/- 2.3*t(.025)(98 df) d. 10 +/- 2.3*t(.025)(100 df) e. none of the above 24. Assume we wish to test whether the dependent variable in a multiple regression model using 5 independent variables (not including seasonal dummies) and 100 observations of quarterly data exhibits seasonality. The SSE for the model with no seasonal dummies = 371. Adding seasonal dummies the SSE drops to 350. The calculated test statistic is: a. 5.46 b. 1.82 c. 1.77 d. the t-value for the first quarter dummy variable e. the average of the t-values for the dummies 25. The Gauss-Markov theorem states least squares estimators are: a. unbiased estimators b. linear estimators c. the most efficient of all possible estimators d. sufficient estimators e. none of the above 26. Testing for the equality of two proportions (large samples) using the standard Normal distribution, the calculated variance of the difference is based on: a. the larger of the two estimated proportions b. the proportion for the larger population c. the weighted average of the two proportions d. the simple average of the two proportions e. none of the above 27. If the seasonal pattern of a time series changes substantially over time: a. seasonal adjustment should be done using dummy variables b. seasonal adjustment should be done using a ratio-to-moving-average approach c. a multiplicative model must be assumed d. an additive model must be assumed e. neither dummies nor ratio-to-moving average work well 28. Autocorrelation and heteroscedasticity: a. make the usual variance formulas inappropriate b. cause the regression parameter estimators to be biased c. fortunately cannot occur simultaneously d. occur only in cross section data e. do not affect t-values 29. Assume that Y and X have a joint bivariate normal distribution, and are positively related with r**2=0.50. Testing whether the slope coefficient in the regression: Y=a+bX+e is significantly different from zero, the calculated test statistic is: a. the square root of (n-2) b. 0.707 c. impossible to find without knowing the variance of b d. non-significant e. none of the above 30. A study of all the firms in the building supply industry two years ago showed that aging the firms accounts receivable resulted in the first column below. Percent of Number of your Age Study accounts firm's accounts less than 30 days 60 80 30 to 60 days 25 30 61 to 90 days 12 35 more than 90 days 3 5 Total 100 150 Last month a sample of 150 accounts from your firm's accounts receivable were aged, with the results shown in the second column above. Testing to see whether your firm differs from the industry average, the calculated test statistic is: a. 11.4 b. 18.7 c. 12.4 d. 7.6 e. 14.2