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 30 40 50 60 70
Mileage 20 24 26 24 20
Make a scatterplot of mileage versus speed. Use a calculator to show that the correlation between speed and mileage is r = 0. Explain why the correlation is 0 even though there is a strong relationship between speed and mileage.