I know many people have talked about this activity for algebra 1 students. I have done it for two years and I absolutely love it. The ultimate goal is to figure out how many elastic bands it will take to drop barbie from the top of the stairs in our back hallway without hurting barbie and yet still giving her a fun ride. I have modified several different worksheets that people have made, including the one from illuminations to make it fit what I want to teach the kids. The goal of the activity is for students to see how linear regression can be applied in a real life situation. I want the students to understand what the y-intercept and slope mean in the context of the problem. Most importantly, I love that the students see that learning can be fun. It is neat that the students from previous years come into my class excited for this one particular activity. Here are some of the links that explain this activity:
http://illuminations.nctm.org/LessonDetail.aspx?id=L646
http://fawnnguyen.com/2012/05/10/barbie-bungee.aspx
http://ispeakmath.org/2012/12/21/introducing-linear-equations-with-barbie-bungee/
This is the worksheet that I use for the project. It is a compilation of worksheets from the above sites: Barbie Bungee Activity
Learning Math is Messy 