# AP Statistics: Introduction to Non-Linear Regression

I’ve been struggling with an interesting way to introduce non-linear regression in AP Statistics. I wanted a quick situation to put my students in to give a reason that non-linear regression is necessary to learn. Then, over the summer, I had an idea while playing video games.

So I nerded out today in class:

Skyrim is a role playing game (and I love good RPGs set in medieval times). Here’s a brief rundown if you need it:

http://en.wikipedia.org/wiki/The_Elder_Scrolls_V:_Skyrim

While playing Skyrim, I noticed that smithing was not leveling up linearly. So I had the brilliant idea to gather some data for my students to explore. I gave my students four pieces of data and asked them how many iron daggers I would need to smith to reach level 100 in smithing.

Here’s what I mean by smithing: http://www.uesp.net/wiki/Skyrim:Smithing

I didn’t inform my students that the data isn’t linear. I didn’t tell them how to approach the problem. I just gave them data and six minutes to make a prediction:

The conversations I heard from my students gave me great insight into their understanding of linear regression. 99% of my students were able to build a least squares regression model and predict that it would take me 516 daggers to reach level 100. There were, however, a few students in each class that looked at the scatter plot and residual plot and decided that their prediction wasn’t accurate. Even with a correlation of r = 0.99, they knew there had a be a better fit.

After a brief class discussion, I informed them that it would take in the neighborhood of 550-560 daggers to reach a level 100 and then showed them a better, non-linear model that gives a more accurate prediction.

The purpose of this activity was to get conversation started about non-linear modeling, and give a context where it could be useful. This activity was meant only as an introduction…now we get to spend three days with logarithms to actually find those models that best fit the data!! Woo! (I’m excited)