572 CHAPTER 10 Correlation and Regression 4.Multiple Regression with Cigarette Contents The table below lists measured amounts (mg) of tar, carbon monoxide (CO), and nicotine in king size cigarettes of different brands (from Data Set 16 “Cigarette Contents” in Appendix B). a. Find the multiple regression equation with the response 1y2 variable of amount of nicotine and predictor 1x2 variables of amounts of tar and carbon monoxide. b. Identify the value of the multiple coefficient of determination R2, the adjusted R2, and the P-value representing the overall significance of the multiple regression equation. c. Use a 0.05 significance level and determine whether the multiple regression equation can be used to predict the amount of nicotine given the amounts of tar and carbon monoxide. d. The Raleigh brand king size cigarette is not included in the table, and it has 23 mg of tar and 15 mg of carbon monoxide. What is the best predicted amount of nicotine? How does the predicted amount compare to the actual amount of 1.3 mg of nicotine? Tar 25 27 20 24 20 20 21 24 CO 18 16 16 16 16 16 14 17 Nicotine 1.5 1.7 1.1 1.6 1.1 1.0 1.2 1.4 Cumulative Review Exercises In Exercises 1–8, based on the nature of the given data, do the following: a. Pose a key question that is relevant to the given data. b. Identify a procedure or tool from this chapter or the preceding chapters to address the key question from part (a). c. Analyze the data and state a conclusion. 1.IQ Scores In the table below, the values of x are IQ scores from randomly selected airline passengers and the values of y are IQ scores from randomly selected police officers. x 105 103 118 137 95 89 89 79 103 103 y 111 108 112 107 108 110 110 109 118 110 2.IQ Scores Use the same table of values from Cumulative Review Exercise 1, but assume that the data are from ten randomly selected college students and for each student, the IQ score is measured before taking a training course and the IQ score is measured again after completion of the course. Each x value is the pre-course IQ score and each y value is the corresponding post-course IQ score. 3.Jockey Weight and IQ Score Use the same table of values from Cumulative Review Exercise 1, but assume that ten professional horse jockeys are randomly selected and their weights (lb) are measured along with the number of times they finished a race in the top three positions (i.e., “in the money”). Each x value is the weight of a horse jockey and each y value is their number of top three race finishes. 4. Digital Buyers A digital buyer is someone who purchases goods and services predominantly online. The table below lists the worldwide numbers (billions) of digital buyers for each of several recent years (based on data from eMarketer). What consequence do the data suggest for the business community? Year 2014 2015 2016 2017 2018 2019 Digital Buyers (billions) 1.32 1.46 1.61 1.77 1.91 2.07
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