Messing with students and regression

A great lesson that makes clear the limitations of extrapolation, via Sarcasymtote:

I was doing a unit on regressions, and so I had everyone collect data. They had to get the shoe size and height of 10 other people in the classroom. They plotted the points and found the line of best fit for height vs shoe size. Because everyone took different data, everyone had different resulting equations. I had them figure out how tall I should be given my shoe size of 12 (which, FUN FACT: is the same size I wore in 7th grade). I seem to have slightly bigger feet than I should, because most people went over my height by a couple inches. But everyone was pretty close, and thank god no one had me at a gangly height of like 6’6″.

Anyways, then I put up this picture. I hadn’t had this great of a reaction in a while. Of course, the first question they all asked was, HOLY SHIT, HOW TALL IS THAT GUY?

I mean, HOLY SHIT. So, I put up this picture too.

Could we predict his height if I gave them the shoe size? He wore a size 37.

They had answers all over the place. 7′ to 12′ was the range, if I remember right. They were really confused. Wait, what did we do wrong?

Nothing.

How can we all be this far off?

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