Online clothes An online clothing retailer keeps track of its customers purchases. For

Chapter 7, Problem 45

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Online clothes An online clothing retailer keeps track of its customers purchases. For those customers who signed up for the companys credit card, the company also has information on the customers Age and Income. A random sample of 500 of these customers shows the following scatterplot of Total Yearly Purchases by Age: e) If a new brand of cigarette contains 7 milligrams of tar T and a nicotine level whose residual is -0.5 mg, what is the nicotine content? 42. Last inning 2010 Refer again to the regression analysis for average attendance and games won by American League baseball teams, seen in Exercise 38. a) Write the equation of the regression line. b) Estimate the Average Attendance for a team with 50 Wins. c) Interpret the meaning of the slope of the regression line in this context. d) In general, what would a negative residual mean in this context? e) The San Francisco Giants, the 2010 World Champions, are not included in these data because they are a National League team. During the 2010 regular season, the Giants won 92 games and averaged 41,736 fans at their home games. Calculate the residual for this team, and explain what it means. 43. Income and housing revisited In Chapter 6, Exercise 32, we learned that the Office of Federal Housing Enterprise Oversight (OFHEO) collects data on various aspects of housing costs around the United States. Heres a scatterplot (by state) of the Housing Cost Index (HCI) versus the Median Family Income (MFI) for the 50 states. The correlation is r = 0.65. The mean HCI is 338.2, with a standard deviation of 116.55. The mean MFI is $46,234, with a standard deviation of $7072.47. 700 600 500 400 300 200 Housing Cost Index 35 40 45 50 55 60 70 Median Family Income (thousands of dollars) a) Is a regression analysis appropriate? Explain. b) What is the equation that predicts Housing Cost Index from median family income? c) For a state with MFI = +44,993, what would be the predicted HCI? d) Washington, DC, has an MFI of $44,993 and an HCI of 548.02. How far off is the prediction in c) from the actual HCI? e) If we standardized both variables, what would be the regression equation that predicts standardized HCI from standardized MFI? f) If we standardized both variables, what would be the regression equation that predicts standardized MFI from standardized HCI? T T 1400 1200 1000 800 600 400 200 0 Total Yearly Purchases (dollars) 20 30 40 50 60 Age The correlation between Total Yearly Purchases and Age is r = 0.037. Summary statistics for the two variables are: a) What is the linear regression equation for predicting Total Yearly Purchase from Age? b) Do the assumptions and conditions for regression appear to be met? c) What is the predicted average Total Yearly Purchase for an 18-year-old? For a 50-year-old? d) What percent of the variability in Total Yearly Purchases is accounted for by this model? e) Do you think the regression might be a useful one for the company? Explain.