AP Statistics: Introducing Extrapolation

4.2 Cautions about Correlation and Regression1_4

Okay, this was the last slide that my classes saw. I wanted you to have a working knowledge of what extrapolation means in statistics.

After we finished our quiz on non-linear regression modeling, I wanted a 15 minute lesson introducing extrapolation. I didn’t want my students to hear me Peanuts teacher a definition and give them several examples that don’t mean anything to them. I’ve tried this…they forget the term approximately 4.87 seconds after they leave my class.

So, instead, we started here:

Age vs Height Data_1

So Coach Helms isn’t the happiest or most photogenic person to use here, but he’s conveniently next door to my room and the kids love him (not to mention he’s a pretty good math teacher).

To answer the question, my students wanted to build a model that relates the age of a person and their height. It was about this time that some people started to have some problems; they started trying to argue that type of model wouldn’t help us. I muttered some quick response (pretending that I didn’t believe them), and we trudged on through some data:

Age vs Height Data_3

Age vs Height Data_4

Age vs Height Data_5

Age vs Height Data_6

Age vs Height Data_7

Age vs Height Data_8

So, the data wasn’t really that creepy in class. I went around our elementary school measuring some students. Real data from real people. I just can’t show you their likeness on a public forum like this; hence why you have creepy smiley faced kids.

I asked my students to use this data to create a prediction model for age vs height. Then I asked them to use that model to predict the heights of a 16, 30 and 50 year old person. More students started to argue that we couldn’t use our model for the 30 and 50 year old…I made them do it any way:

Age vs Height Data_9

They decided that their model was a good predictor of values (they made the argument using the correlation coefficient), but they didn’t believe their predictions for the 30 and 50 year old.

Then we looked at the answers:

Age vs Height Data_10

Age vs Height Data_11

Age vs Height Data_12

As it turns out, their prediction for the 16 year old was pretty accurate, but, as they suspected, it wasn’t for the 30 and 50 year old.

Now is when we defined extrapolation:

4.2 Cautions about Correlation and Regression1_4

We had a nice five minute discussion of what extrapolation is, when it’s used, and whether it’s good or bad (or both). We’ll find out Monday how well it sticks.

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