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WCU ECO 252 - ECO 252 Final Exam

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4/27/01 252x0143 ECO252 QBA2 Name FINAL EXAM Hour of Class Registered (Circle) May 2, 2001 I. (16+ points) Do all the following.1. Hand in your fourth regression problem (2 points) Remember: Y = Company profit in millions of dollars, X1 = CEO's yearly income in thousands of dollars (X1 = 1000 means a million dollar annual income) , X2 = Percentage of stock owed by CEO (X2 = 3 means the CEO owns 3.0% of the stock) Use a significance level of 10% in this problem.2. Answer the following questions.a. For the regression of Y against X1 and X2 only, what does the ANOVA tell us? Which of the coefficients are significant? What tells you this? (3)b. Do an F test to show if the addition of X1 and X3 improves the regression over your results with X2 alone. (4)c. Based on your regression of Y against X1, X2, and X3, (i) What evidence is there that CEO income and stock percentage interact? (1)(ii) What change does this equation predict for every one thousand dollars of CEO income when the CEO owns 5% of the company's stock? (3) (iii) What profit does the equation predict for a firm where the CEO earns $1.2 million and owns40% of the stock? What might this lead you to suspect about this equation? (2)(iv) Based only on the adjusted R-squared and the significance of the coefficients, is there an equation that seems to work better than the equation with three independent variables? Why? (3)4/27/01 252x0143II. Do at least 4 of the following 7 Problems (at least 15 each) (or do sections adding to at least 60 points - Anything extra you do helps, and grades wrap around) . Show your work! State H0 and H1where applicable. Use a significance level of 5% unless noted otherwise. Do not answer questions without citingappropriate statistical tests. 1. (Black, p532) A researcher wishes to predict the price of a meal in New Orleans (y) on the basis of location (1x- a dummy variable, 1 if the restaurant is in the French Quarter, 0 otherwise) and the probability of being seated on arrival. (2x). The data is below (Use )10.. Row price FQ prob y 1x 2x 1 8.52 0 0.62 2 21.45 1 0.43 3 16.18 1 0.58 4 6.21 0 0.74 5 12.19 1 0.19 6 25.62 1 0.49 7 13.90 0 0.80 8 18.66 1 0.75 9 5.25 0 0.37 10 14.85 1 0.32 The following are given to help you.,52.2427,83.1422yy,6,6211xx,1713.3,29.5222xx10 and ?,1651.75?,2121nxxyxyx. You do not need all of these.a. Compute a simple regression of price against 1x.(7)b. On the basis of this regression, what price do you expect to pay for a meal in the French Quarter? Outside the French Quarter? (2)b. Compute 2R(4)c. Compute es (3)d. Compute 0bs( the std deviation of the intercept) and do a confidence interval for 0.(3)f. Do a confidence interval for the price of a meal in the French Quarter. (3) 24/27/01 252x01432. Data from the previous problem is repeated. below . (Use )10.. Row price FQ prob y 1x 2x 1 8.52 0 0.62 2 21.45 1 0.43 3 16.18 1 0.58 4 6.21 0 0.74 5 12.19 1 0.19 6 25.62 1 0.49 7 13.90 0 0.80 8 18.66 1 0.75 9 5.25 0 0.37 10 14.85 1 0.32 The following are given to help you.,52.2427,83.1422yy,6,6211xx,1713.3,29.5222xx10 and ?,1651.75?,2121nxxyxyx. a. Do a multiple regression of price against 1x and 2x. (12)b. Compute R2 and R2 adjusted for degrees of freedom for both this and the previous problem. Compare the values of R2 adjusted between this and the previous problem. Use an F test to compareR2 here with the R2 from the previous problem.(4)c. Compute the regression sum of squares and use it in an F test to test the usefulness of this regression. (5)d. Use your regression to predict the price of a meal in the French Quarter sold when the probability of being seated on arrival is 30%(2)e. Use the directions in the outline to make this estimate into a confidence interval and a prediction interval. (4) 34/27/01 252x01433. An airline wants to select a computer package for its reservation system. Over 20 weeks it tries the four commercially available reservation system packages and records as 1x, 2x, 3x, and 4x, the number of passengers bumped by each system. It will choose the package with the smallest average bumps, assuming that there is a significant difference between the median or average number of bumps. The data below are in the columns labeled x, the original numbers and, in the r columns, their ranks on a 1 to 20 scale. Below this I have given you the sums of the columns, the number of items in each column, the means for each columns and the sums of the squared numbers (ssq) in each column. The columns are independent samples. Use a 5% significance level. Row P1 r1 P2 r2 P3 r3 P4 r4 1x 2x 3x 4x 1 12 15.0 2 2.0 20 20.0 7 7.5 2 14 17.0 4 4.0 9 9.5 6 6.0 3 9 9.5 7 7.5 5 5.0 15 18.0 4 11 13.0 3 3.0 10 11.5 12 15.0 5 16 19.0 1 1.0 12 15.0 6 10 11.5 1x 2x 3x 4x 62.0 17.0 66 40 sum 5 5 6 4 count 12.4 3.4 11 10 mean 798.0 79.0 850 454 ssqa. Assume that the underlying distribution is Normal and test for a significant difference between the means. (7) b. Assume that the underlying distribution is not normal and test for a significant difference between the medians. (5).c. Find the mean and standard deviation for column P3 and test column P3 for a Normal distribution. (5) 44/27/01 252x01434. The data from the previous page is repeated. Use a 5% significance level. Row P1 r1 P2 r2 P3 r3 P4 r4 1x 2x 3x 4x 1 12 15.0 2 2.0 20 20.0 7 7.5 2 14 17.0 4 4.0 9 9.5 6 6.0 3 9 9.5 7 7.5 5 5.0 15 18.0 4 11 13.0 3 3.0 10 11.5 12 15.0 5 16 19.0 1 1.0 12 15.0 6 10 11.5 1x 2x 3x 4x 62.0 17.0 66 40 sum 5 5 6 4 count 12.4 3.4 11 10 mean 798.0 79.0 850 454 ssqa. Assume that the underlying distribution is Normal and test columns 1


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