150 CHAPTER 3 Linear and Quadratic Functions Team On-base Percentage, x Runs Scored, y ( ) x y, Arizona 32.9 812 ( ) 32.9, 812 Atlanta 32.6 732 ( ) 32.6, 732 Chicago Cubs 33.8 822 ( ) 33.8, 822 Cincinnati 32.9 753 ( ) 32.9, 753 Colorado 33.8 824 ( ) 33.8, 824 LA Dodgers 33.4 770 ( ) 33.4, 770 Miami 33.1 778 ( ) 33.1, 778 Milwaukee 32.2 732 ( ) 32.2, 732 NY Mets 32.0 735 ( ) 32.0, 735 Philadelphia 31.5 690 ( ) 31.5, 690 Pittsburgh 31.8 668 ( ) 31.8, 668 San Diego 29.9 604 ( ) 29.9, 604 San Francisco 30.9 639 ( ) 30.9, 639 St. Louis 33.4 761 ( ) 33.4, 761 Washington 33.2 819 ( ) 33.2, 819 Source: espn.com Table 6 (a) To draw a scatter plot, plot the ordered pairs listed in Table 6, with the on-base percentage as the x-coordinate and the runs scored as the y-coordinate. See Figure 6(a). Notice that the points in the scatter plot are not connected. (b) Figure 6(b) shows a scatter plot using a TI-84 Plus CE graphing calculator. (c) The scatter plots show that as the on-base percentage increases, the number of runs scored also increases. Solution (b) TI-84 Plus CE 850 29.5 575 34 Figure 6 29.5 0 30.0 30.5 31.0 31.5 32.0 32.5 33.0 33.5 34.0 Runs Scored versus On-base Percentage in the National League On-base Percentage (a) Runs Scored 825 800 775 750 675 625 650 850 600 725 700 x y Now Work PROBLEM 11(a) 2 Distinguish between Linear and Nonlinear Relations Notice that the points in Figure 6 do not follow a perfect linear relation. However, the data exhibit a linear pattern. There are numerous possible explanations why the data are not perfectly linear, but one easy explanation is the fact that other variables besides on-base percentage (such as number of home runs hit) play a role in determining runs scored. Scatter plots are used to help us to see the type of relation that exists between two variables. In this text, we discuss a variety of different relations that may exist between two variables. For now, we concentrate on distinguishing between linear and nonlinear relations. See Figure 7.
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