4/24/98 252x9842 ECO252 QBA2 Name FINAL EXAM Hour of Class Registered (Circle) April 25, 1998 MWF 10 11 TR 12:30 2:00 I. (16 points) Do all the following.The following pages show the regression of the variable 'pccons', automobile fuel consumed, against someof the following independent variables:'pop' US population in millions'year' Years after 1970 (so 1990 data has 'year' = 20)'earn' Average gross real weekly earnings in 1982 dollars'regpr' Price of regular gasoline in dollars per gallon'relpr' Relative price of gasoline - a price index for gasoline divided by the Consumer Price Index1. In regression 2, what coefficients are significant at the 5% level? Why?(3)2. Which coefficients are significant at the 1% level? Why?(1)3. Comparing the three regressions, noting t-tests, Rsq, Rsq(adj), which seems best? Why?(2)4. Compare the first regression against the third using an F test. Do the added variables have additional explanatory power? (4)5. Using the first observation, give a confidence and prediction interval for consumption. (3)6. In the third equation, are the signs of the coefficients as expected? Why?(2)7. If in 1994 population was 260 million, earnings were $260, regular price was $1.10 and relative price was .650, what consumption does the second regression predict? (2)8. (Extra credit) Looking at the Durbin Watson statistics, explain what they seem to show?(3)4/24/98 252x9842II. Do at least 4 of the following 6 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.1. The data below shows sales in billions, employees in thousands and R&D expenditures in billions y x1x2for a sample of six pharmaceutical corporations..sales empl R&D a) Compute the simple regression equation of sales against employees (6)10.0 43.8 3.47 b) Compute R2. (4)13.4 64.7 1.35 c) Compute se.(3)13.8 49.1 1.20 d) Compute sb0 and do a significance test on b0. (4) 1.3 7.9 0.06 e) Do a confidence interval for sales when a firm has 40 thousand employees.(4)18.8 82.3 1.6316.7 45.2 5.30y y 74 0 1104 02. , . ,x x 1122930 17394. , ,x x 22213 01 46 054. , . ,x y x y x x n1 2 1 218858 672 43 6 ?, . , . and . You do not need all of these.4/24/98 252x98422. Data from 1) is repeated below. y y 74 0 1104 02. , . ,x x 1122930 17394. , ,x x 22213 01 46 054. , . ,x y x y x x n1 2 1 218858 672 43 6 ?, . , . and .a. Do a multiple regression of sales against employment and R&D. (12)b. Compute R2 and R2 adjusted for degrees of freedom. Compare both with values for the previous problem.(5)c. Do an F test to see if R&D helps explain sales.(6)d. Use your equation to predict sales for a firm with 50 thousand employees and $1 billion in R&D expenditures. (2)e. Using the method suggested in the text, make your answer to d into prediction and confidence intervals. (4)4/24/98 252x98423. Data from the previous problem is repeated again! y x1x2a) Compute the correlation between sales and R&D. Is it significant? (5)sales empl R&D b) Compute a rank correlation between sales and R&D. Is it significant?10.0 43.8 3.47 Why might we expect rank correlation to be higher that the conventional13.4 64.7 1.35 correlation? (5)13.8 49.1 1.20 c) Compute Kendall's W for this data and test it for significance.(6) 1.3 7.9 0.0618.8 82.3 1.6316.7 45.2 5.304/24/98 252x98424. Non-union member Confidence in big business and job satisfaction is reported below. a. Test the hypothesis that these are independent.(7) b. Test the hypothesis that the proportion who are very confident is the same for the very satisfied and themoderately satisfied. (4) c. Test the Hypothesis that one third of those who are very satisfied are very confident. (3) very moderatelysatisfied satisfied dissatisfiedVery Confident 111 52 16Somewhat Confident 246 142 55Not Confident 73 51 284/24/98 252x98425. The data below represents samples of consumer ratings of three different displays. Display a. Assuming that each column represents a random sample from a normal1 2 3 population with similar variances, compare the means of the three 55 45 45 populations. (6) 50 30 35 b. Assuming that each row represents the opinions of one individual35 25 20 do a again, still assuming normality.(8)45 35 40 c. Under the assumptions in b, compare the means of display 1 and 240 30 35 using a 2-sample method. (2)x x 112225 10375, ,x x 222165 5675, ,x x 332175 6475, .4/24/98 252x98426. Data from the pervious problem is repeated. Display a. Drop the assumption of normality and compare the medians assuming that1 2 3 that the columns are random samples. (5)55 45 45 b. Do the same assuming that each row is 'owned' by one consumer. (5)50 30 35 c. Since the method used in 6a assumes that variances are similar, test the35 25 20 first two columns to see if they have similar variances (3)45 35 4040 30
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