540 CHAPTER 10 Correlation and Regression Statistical Literacy and Critical Thinking 1. Notation Using the weights (lb) and highway fuel consumption amounts (mi>gal) of the 48 cars listed in Data Set 35 “Car Data” of Appendix B, we get this regression equation: yn = 58.9 - 0.00749x, where x represents weight. a. What does the symbol yn represent? b. What are the specific values of the slope and y-intercept of the regression line? c. What is the predictor variable? d. Assuming that there is a significant linear correlation between weight and highway fuel consumption, what is the best predicted value of highway fuel consumption of a car that weighs 3000 lb? 2. Notation What is the difference between the regression equation yn = b 0 + b1x and the regression equation y = b0 + b1x? 3.Best-Fit Line a. What is a residual? b. In what sense is the regression line the straight line that “best” fits the points in a scatterplot? 4.Correlation and Slope What is the relationship between the linear correlation coefficient r and the slope b1 of a regression line? Making Predictions. In Exercises 5–8, let the predictor variable x be the first variable given. Use the given data to find the regression equation and the best predicted value of the response variable. Be sure to follow the prediction procedure summarized in Figure 10-5 on page 533. Use a 0.05 significance level. 5.Cars For the 12 small cars included in Data Set 35 “Car Data” from Appendix B, the weights of the cars 1x2 are paired with the highway fuel consumption 1y2. The 12 paired values yield x = 2817.7 lb, y = 37.3mi>gal, r = -0.395, P@value = 0.203, and the regression equation is yn = 53.7 - 0.00580x. Find the best predicted value of the highway fuel consumption for a small car that weighs 2500 lb. 6.Bear Measurements Head widths (in.) and weights (lb) were measured for 20 randomly selected bears (from Data Set 18 “Bear Measurements” in Appendix B). The 20 pairs of measurements yield x = 6.9 in., y = 214.3 lb, r = 0.879, P-value = 0.000, and yn = -212 + 61.9x. Find the best predicted weight of a bear given that the bear has a head width of 6.5 in. 7.Height and Weight Heights (cm) and weights (kg) are measured for 100 randomly selected adult males (from Data Set 1 “Body Data” in Appendix B). The 100 paired measurements yield x = 173.79 cm, y = 85.93 kg, r = 0.418, P-value = 0.000, and yn = -106 + 1.10x. Find the best predicted weight given an adult male who is 180 cm tall. 8. Cigarette Tar and Nicotine For 25 king-size cigarettes listed in Data Set 16 “Cigarette Contents” in Appendix B, the amount 1x2 of tar (mg) and the amount 1y2 of nicotine (mg) are listed for each cigarette. The 25 paired amounts yield x = 21.1mg, y = 1.26mg, r = 0.245, P@value = 0.237, and the regression equation is yn = 0.883 + 0.0177x. Find the best predicted amount of nicotine for a cigarette with 10 mg of tar. Finding the Equation of the Regression Line. In Exercises 9 and 10, use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. 9. 10-2 Basic Skills and Concepts x 10 8 13 9 11 14 6 4 12 7 5 y 9.14 8.14 8.74 8.77 9.26 8.10 6.13 3.10 9.13 7.26 4.74
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