15 What are causal models?

A causal relationship is useful for making predictions about the consequences of changing circumstances or policies; it tells us what would happen in alternative (or counterfactual) worlds."

Some examples of statistical relationships might include:

• Height and weight — as height increases, you’d expect weight to increase, but not perfectly.
• Alcohol consumed and blood alcohol content — as alcohol consumption increases, you’d expect one’s blood alcohol content to increase, but not perfectly.
• Vital lung capacity and pack-years of smoking — as amount of smoking increases (as quantified by the number of pack-years of smoking), you’d expect lung function (as quantified by vital lung capacity) to decrease, but not perfectly.
• Driving speed and gas mileage — as driving speed increases, you’d expect gas mileage to decrease, but not perfectly.

So let’s study statistical relationships between one response variable y and one predictor variable x!