Question

Shawna reads a scatterplot that displays the relationship between the number of cars owned per household and the average number of citizens who have health insurance in neighborhoods across the country. The plot shows a strong positive correlation.

Shawna recalls that correlation does not imply causation. In this example, Shawna sees that increasing the number of cars per household would not cause members of her community to purchase health insurance.
Identify the lurking variable that is causing an increase in both the number of cars owned and the average number of citizens with health insurance.
A) Average income per household
B) The number of cars on the road
C) The number of citizens in the United States
D) Average mileage per vehicle

Answer 1

The correct answer is:

A) Average income per household

Explanation:

Correlation of variables is the statistical relationship between two variables. A correlation is positive if both variables move in the same direction (e.g both are increasing, or both are decreasing), and negative if the variables move in different directions - as one variable increases, the other decreases.

Correlation does not imply causation: This means that one can not legitimately associate a cause-and-effect relationship between the two variables, especially when there is a third variable (lurking) that has an effect on the outcomes that is not included as an explanatory or response variable.

In this example, it cannot be legitimately shown that increasing the number of cars per household would cause members of the community members to purchase health insurance, but when we bring in the lurking variable, which is the increase in average income per household, we can see that this possibility might cause more people to buy more health insurance even after they have purchased cars, because they have more money to spend.