We are asked to show an example of two data sets being correlated but not having a causal relationship. Let's start by recalling what these concepts are.
Correlation: Two data sets are correlated when the y values tend to increase or decrease as the x values increase. If they increase we call it a positive correlation, and if they decrease we say that it is a negative correlation.
Postive Correlation
Negative Correlation
Causation: Causation, on the other hand, implies that a change in one quantity causes a change in the second quantity. A correlation between quantities does not always imply causation.
Example Solution
If we consider the amount of cinemas in a city compared to the amount of hospitals as the city grows, we can realize that these quantities are correlated but do not have a causal relationship.
As a city increases in size, the amount of hospitals and cinemas would both increase. Therefore they are correlated, as when one increases or decreases the other will tend to do the same.
The amount of cinemas does not affect the amount of hospitals. Notice that changing the amount of cinemas will not change the amount of hospitals. Therefore, they do not have a causal relationship.
