I applied for and received a grant this year that allowed me to purchase an XBox One with Kinect for my AP Statistics class. I think lots of people thought I was a crazy person, but I can't really determine a better way for kids to really understand data and different statistical ideas than creating their own data through a medium they are deeply familiar with and are curious about.
I received the materials and games I'd purchased before Christmas. During break, I wrote our first activity using the console. We are in the last few days of the regression unit, and so I wrote a Forza project to help kids review the main concepts of linear regression.
I purchased Forza 5 and decided that it would be fairly easy to do a linear regression of lap time versus placement. The premise is that the management of the particular track I selected is interested in developing a model for future aspiring drivers. The purpose of the model is to predict the ability of these aspiring drivers to compete on the current circuit, and particularly at the track I chose.
Each of my students received a letter from the track management team to both sign up as a driver and to work on the statistical analysis for the project.
Kids signed up for an after-school timeslot to complete a test lap. I used Sign Up Genius to do this.
The kids completed one practice lap and then completed their timed trial. We recorded each person's placement and time in a Google Form.
After I had all the data, I did a little regression analysis myself. I threw out all my kids that were last (there were 16 total racers on each lap). You'll see that in my write-up, I ask kids to ponder WHY I did that. If you think about it, it makes sense. You could barely be in 16th place, or you could order a pizza, take a shower, drink a pop, and still be 16th.
When I did the regression with sixteenths removed, it was very clear that there were two separate linear patterns, and when analyzed, they were very interesting. It turns out that the game went MUCH easier on the first four racers (this was on a brand new game/console post-tutorial races). When you remove those, it's obvious that post the introductory races, the pattern is incredibly linear. I forget the values, but I'm thinking that the coefficient of determination was somewhere around 97.8% with a lovely residual plot.
Here is the write-up the kids are assigned:
Almost all the kids have LOVED this project, and having this self-created data that they are genuinely interested really boosts the inquiry and depth of thought/analysis.
Even more fun is when one classmate races DURING class, we use our model to predict his/her placement and then calculate the residual. So. Much. Fun.
I hope this is the first of many AP Stats projects using the XBox. If you have any thoughts as to others I might do (especially in inference), help a girl out and let me know!
Note: If you decide to do this project, I left a few important things off of the handout. (1) Have students describe the scatterplot (2) Have students interpret the y-intercept (3) Have students analyze residual plot for fit.