Describe an example in which two variables are strongly correlated, but changes in one do not cause changes in the other. For example, a group of elementary school children took a vocabulary test. It turned out that children with larger shoe sizes tended to get higher scores on the test, and those with smaller shoe sizes tended to get lower scores. As a result, there was a large positive correlation between vocabulary and shoe size. Does this mean that learning new words causes one's feet to grow, or that growing feet cause one's vocabulary to increase? Obviously not. There is a third factoragethat is related to both shoe size and vocabulary.