The Wandering Point, Updated

One of my favorite activities from the Stats: Modeling the World teaching materials is "The Wandering Point" class activity to look at the influence of points on correlation and linear regression. My students always get a lot of out it and I think it lends itself to a high level of student engagement. I have since adapted* this activity to incorporate the new regression function of Desmos as well as some modifications to enhance student understanding.

"The Wandering Point" activity essentially has students explore the changes to the linear regression model and correlation when a fifth "wandering" point is added to a set of four fixed points. I left the original idea of the four points as well as the requested changes to the fifth point. The students are asked to use the Desmos interactive worksheet to find the correlation and slope of the LSRL as well as make an estimate of the residual and leverage for each possible fifth wandering point.

Student worksheet for my updated activity: The Wandering Point, Updated
To be used with the Desmos interactive worksheet: The Wandering Point, Updated

I field tested this today and got an overall positive review from my students. They, as well as a colleague or two, made some nice constructive suggestions (for example, estimating what kind of leverage each wandering point has) and I have included those as well. If you are familiar with the original activity, you'll perhaps notice some of the other changes I made. The Desmos sliders make it easy to change the wandering point to the suggested points as well as any others that a student desires to help them explore the questions.

I think the ability of the Desmos worksheet to help animate points in the plane is a powerful use of the technology. Even more importantly, the output from the Desmos worksheet allows students to find the calculated values easily. With the deemphasis on the computational aspect of the regression model, it allows time to have students answer some questions to help facilitate their understanding.

*This activity is based on and adapted from the copyrighted Bock, Velleman, and De Veaux Stats: Modeling the World class activity “The Wandering Point” with permission of the lead author.