# Linear Regression for Normal People

## A quick-ish way to see and understand how statisticians use linear regression.

Suppose I give you these data on height and weight of 50 people. The data are fake, so don’t get too excited. Next, I ask you if there is any relationship between the height and weight of people. From your experience, you probably will say yes, height is related to weight. The taller the person, the heavier they are. But I counter that I know short people who weigh more than their taller counterparts.

How do you prove to me statistically that taller people weigh more than shorter ones?

## Step One: The Eyeball Test

One of the first things you can do is plot the data on a scatter plot:

We can both see that the scatter of the points gets higher in weight as the height increases left to right. You can say to me, “See? The higher the weight, the higher the height, and vice-versa!” But what if I counter by telling you that there are some points indicating lighter-but-taller?