SECTION 9.2 Linear Regression 491 Using and Interpreting Concepts Finding the Equation of a Regression Line In Exercises 17–26, find the equation of the regression line for the data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. If convenient, use technology. 17. Height and Number of Stories The heights (in feet) and the numbers of stories of the nine tallest buildings in Houston, Texas (Source: Emporis Corporation) Height, x 1002 992 901 780 762 756 752 741 735 Stories, y 75 71 64 56 53 55 48 47 47 (a) x = 950 feet (b) x = 850 feet (c) x = 800 feet (d) x = 650 feet 18. Square Footage and Home Sale Price The square footages and sale prices (in thousands of dollars) of nine homes in Akron, Ohio, are shown in the table at the left. (Source: Howard Hanna) (a) x = 1100 square feet (b) x = 725 square feet (c) x = 2575 square feet (d) x = 950 square feet 19. Hours Studying and Test Scores The number of hours 9 students spent studying for a test and their scores on that test Hours spent studying, x 0 2 4 5 5 5 6 7 8 Test scores, y 40 51 64 69 73 75 93 90 95 (a) x = 3 hours (b) x = 6.5 hours (c) x = 13 hours (d) x = 4.5 hours 20. Goal Differential and Wins The goal differential (goals scored minus goals conceded) and the number of wins for the top 10 teams in the 2020–2021 English Premier League season (Source: Premier League) Goal differential, x 5129262218152316 8 -1 Wins, y 27 21 20 19 20 19 18 18 18 17 (a) x = 0 goals (b) x = 20 goals (c) x = 40 goals (d) x = 60 goals 21. Heart Rate and QT Interval The heart rates (in beats per minute) and QT intervals (in milliseconds) for 13 males (The figure at the left shows the QT interval of a heartbeat in an electrocardiogram.) (Adapted from Chest) Heart rate, x 60 75 62 68 84 97 66 QT interval, y 403 363 381 367 341 317 401 Heart rate, x 65 86 78 93 75 88 QT interval, y 384 342 377 329 377 349 (a) x = 120 beats per minute (b) x = 67 beats per minute (c) x = 90 beats per minute (d) x = 83 beats per minute Electrocardiogram QT Interval The QT interval is a measure of electrical waves of the heart. A lengthened QT interval can indicate heart health problems. FIGURE FOR EXERCISE 21 Square footage, x Sale price, y 1438 120.0 1280 109.5 1680 289.0 5627 915.0 1040 49.9 1180 79.9 876 59.9 1552 94.9 2180 199.9 TABLE FOR EXERCISE 18
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