Question

Give an example of data that could be obtained to make a prediction. Discuss lurking variables and why the correlation may not imply causation.

Correlation and Regression is typically most students’ favorite area in statistics because it gives the ability to make predictions. Give an example of data that could be obtained to make a prediction. Discuss lurking variables and why the correlation may not imply causation.

Answer 1

The scatterplot below shows the relationship between the number of firefighters sent to fires (x) and the amount of damage caused by fires (y) in a certain city.

25ООООО 2DDDDDD Damage ($) 15ООООО 1ОООООО БООООО о 10 40 20 30 # of Firefighters

The scatterplot shows a positive association with a somewhat strong curvilinear form. An increase in the number of firefighters is associated with an increase in the damage done by the fire.

Can we conclude that the increase in firefighters causes the increase in damage? Of course not.

A third variable is at play in the background – the seriousness of the fire – and is responsible for the observed relationship. More serious fires require more firefighters and also result in more damage.

The following figure will help you visualize this situation:

lurking variable Seriousness of the fire cause cause Number of firefighters > Amount of damage ) observed association

The seriousness of the fire is a lurking variable. A lurking variable is a variable that is not measured in the study. It is a third variable that is neither the explanatory nor the response variable, but it affects your interpretation of the relationship between the explanatory and response variables.

In our example, the lurking variable has an effect on both the explanatory and the response variables. This common effect creates the observed association between the explanatory and response variables even though there is no cause-and-effect link between them.

Correlation is a statistical technique which tells us how strongly the pair of variables are linearly related and change together. It does not tell us why and how behind the relationship but it just says the relationship exists.

Causation takes a step further than correlation. It says any change in the value of one variable will cause a change in the value of another variable, which means one variable makes other to happen. It is also referred as cause and effect.

So now we know what correlation and causation is, it’s time to understand “Correlation does not imply causation!” with a famous example.

Ice cream sales is correlated with homicides in New York (Study)

As the sales of ice cream rise and fall, so do the number of homicides. Does the consumption of ice cream causing the death of the people?

No. Two things are correlated doesn’t mean one causes other.

Correlation does not mean causality or in our example, ice cream is not causing the death of people.

When 2 unrelated things tied together, so these can be either bound by causality or correlation.

In Majority of the cases correlation, are just because of the coincidences. Just because it seems like one factor is influencing the other, it doesn’t mean that it’s actually does.

Just after finding correlation, don’t draw the conclusion too quickly. Take time to find other underlying factors as correlation is just the first step. Find the hidden factors, verify if they are correct and then conclude.