516 CHAPTER 10 Correlation and Regression INTERPRETATION It appears that there is a linear correlation between lottery jackpot amounts and numbers of tickets sold. It appears that higher jackpots correspond to more tickets sold. In addition to the numbers, common sense and critical thinking also support this finding. Although we have found a linear correlation, we should not conclude that one of the variables is a cause of the other. It is reasonable to believe that larger jackpots cause higher ticket sales, but that belief is not justified by the statistical analysis. Correlation does not imply causation. YOUR TURN. Do Exercise 15 “Taxis.” Correlation 0 −1 1 No correlation Correlation Sample Data: r = 0.947 r = 0.666 Critical Value r = −0.666 Critical Value FIGURE 10-3 Critical r Values and the Computed r Value TABLE 10-4 U.S. Margarine Consumption and Divorces in Maine Margarine 8.2 7.0 6.5 5.3 5.2 4.0 4.6 4.5 4.2 3.7 Divorces 5.0 4.7 4.6 4.4 4.3 4.1 4.2 4.2 4.2 4.1 Spurious Correlation EXAMPLE 5 Table 10-4 lists paired data consisting of per capita consumption of margarine (pounds) in the United States and the divorce rate in Maine (divorces per 1000 people in Maine). Each pair of data is from a different year. The data are from the U.S. Census Bureau and the U.S. Department of Agriculture. Is there a linear correlation? What do you conclude? YOUR TURN. Do Exercise 25 “Car Sales and the Super Bowl.” SOLUTION Here are the key points about the data in Table 10-4: ■ The requirements appear to be satisfied. ■ A scatterplot shows a very clear pattern of points that is close to a straight-line pattern, and there are no outliers. ■ The linear correlation coefficient r is equal to 0.993. ■ The P-value is 0.000. ■ The critical values are r = {0.632 (assuming a 0.05 significance level). Based on these results, we should support a claim that there is a linear correlation between margarine consumption and the divorce rate in Maine. But, come on! Common sense strongly suggests that there is no real association between those two variables. It would be totally ridiculous to argue that one of the variables is the cause of the other. Statistics is so much more than blindly running data through formulas and procedures—it requires critical thinking! Go Figure 300,000: The average number of items in a home in America.
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