469 Where You’ve Been In Chapters 1– 8, you studied descriptive statistics, probability, and inferential statistics. One of the techniques you learned in descriptive statistics was graphing paired data with a scatter plot (see Section 2.2). For instance, the salaries and average home game attendances for the teams in Major League Baseball in a recent year are shown in the scatter plot at the right and in the table below. Average home game attendance Salary (in millions of dollars) y x Major League Baseball 50 100 150 200 250 10,000 20,000 30,000 40,000 50,000 Where You’re Going In this chapter, you will study how to describe and test the significance of relationships between two variables when data are presented as ordered pairs. For instance, in the scatter plot above, it appears that higher team salaries tend to correspond to higher average attendances and lower team salaries tend to correspond to lower average attendances. This relationship is described by saying that the team salaries are positively correlated to the average attendances. Graphically, the relationship can be described by drawing a line, called a regression line, that fits the points as closely as possible, as shown below. The second scatter plot below shows the salaries and wins for the teams in Major League Baseball in the same year. From the scatter plot, it appears that there is a weak positive correlation between the team salaries and wins. Average home game attendance Salary (in millions of dollars) y x Major League Baseball 50 100 150 200 250 10,000 20,000 30,000 40,000 50,000 Wins Salary (in millions of dollars) y x Major League Baseball 50 100 150 200 250 40 50 60 70 80 90 100 110 Salary (in millions of dollars) 124.0 133.2 82.7 219.0 217.8 80.8 109.7 151.3 145.3 100.6 Average home game attendance 26,364 32,777 16,146 35,994 38,208 20,622 22,334 21,465 36,954 18,536 Salary (in millions of dollars) 166.0 98.2 177.3 193.6 74.7 128.8 113.8 154.8 228.4 102.9 Average home game attendance 35,276 18,267 37,321 49,066 10,016 36,091 28,436 30,155 40,795 20,626 Salary (in millions of dollars) 141.8 72.9 90.3 126.9 175.6 161.1 56.1 104.4 64.7 203.0 Average home game attendance 33,672 18,413 29,585 22,112 33,429 42,968 14,552 26,333 21,607 27,899
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