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Describe correlation EXAMPLE 1 Telephones Describe the correlation shown by each scatter plot.

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Describe correlation EXAMPLE 1 SOLUTION The first scatter plot shows a positive correlation, because as the number of cellular phone subscribers increased, the number of cellular service regions tended to increase. The second scatter plot shows a negative correlation, because as the number of cellular phone subscribers increased, corded phone sales tended to decrease.

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EXAMPLE 2 Estimate correlation coefficients Tell whether the correlation coefficient for the data is closest to – 1, – 0.5, 0, 0.5, or 1. a.a. SOLUTION a. The scatter plot shows a clear but fairly weak negative correlation. So, r is between 0 and – 1, but not too close to either one. The best estimate given is r = – 0.5. ( The actual value is r – 0.46. )

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Estimate correlation coefficients EXAMPLE 2 b. The scatter plot shows approximately no correlation. So, the best estimate given is r = 0. (The actual value is r – 0.02.) SOLUTION b.

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Estimate correlation coefficients EXAMPLE 2 c. c. The scatter plot shows a strong positive correlation. So, the best estimate given is r = 1. (The actual value is r 0.98.) SOLUTION

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GUIDED PRACTICE for Examples 1 and 2 For each scatter plot, (a) tell whether the data have a positive correlation, a negative correlation, or approximately no correlation, and (b) tell whether the correlation coefficient is closest to –1, – 0.5, 0, 0.5, or 1. 1.

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GUIDED PRACTICE for Examples 1 and 2 SOLUTION (a) The scatter plot shows a positive correlation. (b) The best estimate given is r = 0.5.

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GUIDED PRACTICE for Examples 1 and 2 For each scatter plot, (a) tell whether the data have a positive correlation, a negative correlation, or approximately no correlation, and (b) tell whether the correlation coefficient is closest to –1, – 0.5, 0, 0.5, or 1. 2.

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GUIDED PRACTICE for Examples 1 and 2 SOLUTION (a) The scatter plot shows a strong negative correlation. So the best estimate given is r is –1. (b) The best estimate given is r = –1.

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GUIDED PRACTICE for Examples 1 and 2 For each scatter plot, (a) tell whether the data have a positive correlation, a negative correlation, or approximately no correlation, and (b) tell whether the correlation coefficient is closest to –1, – 0.5, 0, 0.5, or 1. 3.

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GUIDED PRACTICE for Examples 1 and 2 SOLUTION (a) The scatter plot shows approximately no correlation. (b) The best estimate given is r = 0.

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