Think About It: If there is a cause-effect relationship between two variables, it is not always clear which variable causes which. For example, suppose there is a moderate positive relationship between the number of years employees work at a company and their happiness level with their jobs. Do the jobs make them happy, or do happy people stay with their jobs longer?

Finally, a correlation can be purely coincidental. Suppose a correlation is found between the number of running races a city holds and the number of broken parking meters in the city. This correlation is likely to be just a coincidence. There’s no reason to think one would have any effect on the other, and there are no apparent lurking variables.

First statement: The lurking variable is population. Cities with greater populations will have greater cell phone sales and greater numbers of people who have cavities to be filled.

If there's a causation, then there's a cause-effect relationship between the variables.

Second statement: Plants need water. Using more water creates a more expensive water bill.

Third statement: Warm temperatures melt snow. This is causation.

If there's neither a causation nor a lurking variable, choose coincidence.

Fourth statement: There is no reason for a cause-effect relationship and no reasonable lurking variable.

The warmer it is, the more people eat ice cream and the more people wear sandals.

The older a child is, the more capable the child is at sports and the more education the child received in reading.

The distance a hiker travels is a lurking variable. It seems reasonable that the greater the distance a hiker hikes, the longer he is exposed to bugs that may bite him. Answer True for this potential variable.

The hiker’s favorite music does not affect the number of granola bars he consumes or the number of bug bites he may receive. It is not even clear if the hiker listens to music while hiking. Answer False for this potential variable.

The type of hiking boots a hiker wears does not affect the number of granola bars he consumes or the number of bug bites he may receive. Answer False for this potential variable.

The amount of time the hiker travels is a lurking variable. The longer a hiker is exposed to bugs, the more bug bites the hiker is likely to receive. Answer True for this potential variable.

A correlation is an association. It is sometimes a cause-effect relationship. There may also be lurking variables.

Determine the most likely lurking variable in the strong positive correlation between the number of umbrellas sold and the water level in nearby rivers.

A melting glacier upstream would not lead to an increase in umbrella sales but may lead to an increase in water levels in nearby streams. This choice is not a lurking variable.

A large number of tourists in the area may lead to an increase in umbrella sales but is not related to a change in water levels in nearby streams. This is not a lurking variable.

Rainfall would affect both the number of umbrellas sold and the water level of nearby streams. As the number of umbrellas sold increases, the level of rainfall would likely increase and the water levels of nearby streams would increase.

The correct answer is high levels of rainfall.

A new shopping mall in the area may lead to an increase in umbrella sales but is not related to a change in water levels in nearby streams. This is not a lurking variable.

It seems reasonable that an increase in the amount of fertilizer a homeowner uses leads to an increase in the height of plants in her garden and that the increase in fertilizer caused this relationship. The correlation is most likely a causation.