What is an associated variable?

Two variables are associated (and not independent) if some of the variability in one variable can be explained by the other variable.

For example, a battery producer wants to know whether its product is used most often in cars or in boats. The following table shows the counts for batteries sold for use in boats and cars in Columbus, Ohio and Portsmouth, New Hampshire.
City Boat Car
Columbus 20 300
Portsmouth 120 50

You cannot summarize the battery usage in the two cities in the same way. In Portsmouth, people use more batteries in boats than in cars. However, in Columbus, people use many more batteries in cars than in boats. The variables are associated because the distribution of observations for vehicle differs depending on the city.

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