Sarah described the following situation: when more apples grew in the backyard, the pet cat stayed indoors for a longer time. which of the following best describes the situation? this is an example of correlation but not causation. this is an example of causation but not correlation. this is an example of both correlation and causation. this is an example of neither correlation nor causation.

This is an example of correlation but not causation.

Explanation:

The statement "when more apples grew in the backyard, the pet cat stayed indoors for a longer time" is an excellent example to explain the difference between causation and correlation.

Is the very fact that the apples grew in the backyard what makes the pet cat stay indoors longer?

Sure, you know it isn't. Sure there is another cause that influence both the growing of apples and the time the pet cats stay indoor. So, there is not a causality relationship.

Given that some fact is influencing both phenomena, you find that they behave in a way that one permits predict the other, which is what correlation indicates, but not that one is the cause of the other.

When you know the cause you might change the final behavior, but when you know that the variables are correlated you just can use one to predict the other.

In this example, if you see that more apples grow in the backyard you can predict that the cat pets will stay indoors for a longer time, but you can do nothing to modify the time the pet cats stay indoors because you do not the reason why they are doing that.