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 owns 40 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 252x0143 II 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 H 0 and H1 where applicable Use a significance level of 5 unless noted otherwise Do not answer questions without citing appropriate statistical tests 1 Black p532 A researcher wishes to predict the price of a meal in New Orleans y on the basis of location x1 a dummy variable 1 if the restaurant is in the French Quarter 0 otherwise and the probability of being seated on arrival x 2 The data is below Use 10 Row price FQ y prob x1 x2 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 y 142 83 y x 1y x 2 2 2427 52 y 75 1651 x x 1 x2 1 6 x 2 1 6 x 2 5 29 x 2 2 3 1713 and n 10 You do not need all of these a Compute a simple regression of price against x1 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 R 2 4 c Compute s e 3 d Compute s b0 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 2 4 27 01 252x0143 2 Data from the previous problem is repeated below Use 10 Row 1 price FQ y prob x1 x2 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 y 142 83 y x 1y x 2 2 2427 52 y 75 1651 x x 1 x2 1 6 x 2 1 6 x 2 5 29 x 2 2 3 1713 and n 10 a Do a multiple regression of price against x1 and x 2 12 b Compute R 2 and R 2 adjusted for degrees of freedom for both this and the previous problem Compare the values of R 2 adjusted between this and the previous problem Use an F test to compare R 2 here with the R 2 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 3 4 27 01 252x0143 3 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 x1 x 2 x 3 and x 4 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 x1 1 2 3 4 5 6 12 14 9 11 16 x1 62 0 5 12 4 798 0 r2 P3 2 0 4 0 7 5 3 0 1 0 20 9 5 10 12 10 x2 15 0 17 0 9 5 13 0 19 0 2 4 7 3 1 x2 17 0 5 3 4 79 0 P4 20 0 9 5 5 0 11 5 15 0 11 5 7 6 15 12 x3 x3 66 6 11 850 r3 r4 x4 7 5 6 0 18 0 15 0 x4 40 4 10 454 sum count mean ssq a 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 4 4 27 01 252x0143 4 The data from the previous page is repeated Use a 5 significance level Row P1 r1 P2 x1 1 2 3 4 5 6 12 14 9 11 16 x1 62 0 5 12 4 798 0 r2 P3 2 0 4 0 7 5 3 0 1 0 20 9 5 10 12 10 …
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