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The Practice of Statistics | 5th Edition | ISBN: 9781464108730 | Authors: Daren S. Starnes, Josh Tabor
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Strong association but no correlation The gas mileage of an automobile first increases

Chapter 3, Problem 25

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QUESTION:

Strong association but no correlation The gas mileage of an automobile first increases and then decreases as the speed increases. Suppose that this relationship is very regular, as shown by the following data on speed (miles per hour) and mileage (miles per gallon). Speed: 20 30 40 50 60 Mileage: 24 28 30 28 24 (a) Make a scatterplot to show the relationship between speed and mileage. (b) Calculate the correlation for these data by hand or using technology. (c) Explain why the correlation has the value found in part (b) even though there is a strong relationship between speed and mileage.

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QUESTION:

Strong association but no correlation The gas mileage of an automobile first increases and then decreases as the speed increases. Suppose that this relationship is very regular, as shown by the following data on speed (miles per hour) and mileage (miles per gallon). Speed: 20 30 40 50 60 Mileage: 24 28 30 28 24 (a) Make a scatterplot to show the relationship between speed and mileage. (b) Calculate the correlation for these data by hand or using technology. (c) Explain why the correlation has the value found in part (b) even though there is a strong relationship between speed and mileage.

ANSWER:

Step 1 of 5

Given,

No. of data points,

We have to assume that the relationship between the speed and mileage in this data is very regular.

 

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