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Chapter 3: Q.26 (page 162)

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). Make a scatterplot of mileage versus speed.

The correlation between speed and mileage isr=0. Explain why the correlation is 0 even though there is a strong relationship between speed and mileage.

Short Answer

Expert verified

The linear correlation coefficient is 0, because there is no LINEAR pattern in the scatterplot and the linear correlation coefficient only measures a linear pattern.

Step by step solution

01

Given Information

The speed and mileage have ar=0correlation.

02

Explanation 

The horizontal axis represents speed, while the vertical axis represents mileage.

03

Conclusion

The correlation is set to 0, indicating that there is no linear correlation.

The speed and mileage have a perfect quadratic relationship.

Because there is no LINEAR pattern in the scatterplot and the linear correlation coefficient only assesses a linear pattern, the linear correlation coefficient is 0.

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