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 some of 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 Index 1 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 252x9842 II 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 H 0 and H1 where 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 x1 x2 for 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 R 2 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 4 18 8 16 7 7 9 0 06 82 3 45 2 1 63 5 30 e Do a confidence interval for sales when a firm has 40 thousand employees y 74 0 y 1104 0 x 293 0 x 17394 x 13 01 x 46 054 x y x y 188 58 x x 672 43 and n 6 You do not need all of these 2 1 1 2 1 2 2 1 2 2 2 4 24 98 252x9842 2 Data from 1 is repeated below y 74 0 y 1104 0 x 293 0 x 17394 x x y x y 188 58 x x 672 43 and n 6 2 1 1 2 2 1 2 13 01 x 2 2 46 054 1 2 a Do a multiple regression of sales against employment and R D 12 b Compute R 2 and R 2 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 252x9842 3 Data from the previous problem is repeated again y x1 x2 a 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 conventional 13 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 06 18 8 82 3 1 63 16 7 45 2 5 30 4 24 98 252x9842 4 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 the moderately satisfied 4 c Test the Hypothesis that one third of those who are very satisfied are very confident 3 very moderately satisfied satisfied dissatisfied Very Confident 111 52 16 Somewhat Confident 246 142 55 Not Confident 73 51 28 4 24 98 252x9842 5 The data below represents samples of consumer ratings of three different displays Display a Assuming that each column represents a random sample from a normal 1 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 individual 35 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 2 40 30 35 using a 2 sample method 2 x 1 225 x 2 1 10375 x 2 165 x 2 2 5675 x 3 175 x 2 3 6475 4 24 98 252x9842 6 Data from the pervious problem is repeated Display a Drop the assumption of normality and compare the medians assuming that 1 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 the 35 25 20 first two columns to see if they have similar variances 3 45 35 40 40 30 35
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