Generating Data for Regressions

My AP Statistics class is now entering a phase of exploring associations between two quantitative variables. We've been looking at scatter plots and discussing what the plot indicates about association. We also discussed how to draw an ellipse around a scatter plot and use the major and minor axes of the ellipse to estimate the absolute value of the correlation. (For those of you who have never done this, if L is the major axis and W is the minor axis then (L - W) / L provides a very good estimate, easily within 0.2 of the correlation.)

I have developed or borrowed a few data collection activities that are easy to do, engage students, and provide reasonable data for use in describing scatter plots and in creating linear regression models.

ORBIT EXPRESS
This is an activity that I modified from a session I attended at the NCTM Conference. The original was presented as an experiment to test two different materials. I do the original as well, while working through experimental design, but focus on a single material and measure drops from different heights.

The scenario is that students work in the design and analysis department for Orbit Express, a package delivery company that will delivery packages by dropping them from orbit. Take a sheet of paper and wad it up; this is the delivery vehicle. Students have to measure six drops from different heights. They drop toward a target on the floor (a coin or piece of tape works well). They measure the height of the drop and the distance of the delivery vehicle from the target once the delivery vehicle has come to rest.

CAR MILEAGE
I don't recall where this one came from, I think it came from a book, so I apologize in advance for not citing the source. (If you happen to know, contact me and I will rectify the citation issue). In this activity, students record the year of car and the mileage for the primary vehicle that they drive. This provides some interesting discussions once a regression model is built as to the meaning of the y-intercept and the slope in context of the situation.

DA VINCI'S VITRUVIAN MAN
Another activity that I forget the source. Da Vinci's sketch the Vitruvian Man indicates that a person's arm span is equal to that person's height. The natural question is to ask whether or not Da Vinci was correct. Students measure their height and arm span length and take a look. This also provides a basis for regression inference in terms of a confidence interval for the slope. Ask students which is the explanatory variable and which the response variable. It gets them thinking about what is happening in the context of the situation. Discuss how applicable the model is for different heights.

PASS THE BUCK
This activity came from a pre-AP session provided by my school district. In this scenario, three students pass a buck (I use a 3" x 5" card) from hand-to-hand as quickly as they can. After coming to agreement as a class as to what constitutes a pass, the method of passing, and other measurement conditions, we start accumulating data. The first person in line holds the buck and says, "Go." A timer starts timing at that moment. The buck is quickly passed from person to person. When the last person has possession of the buck the yell, "Stop!" and the timer stops timing. The number of people in line and the time it took them to pass the buck are recorded. Three more students join the line and the process is repeated. Continue until the entire class, except for the timer, are in the line. It's a fun activity that leads to some interesting discussions. First, students are used to using time as the explanatory variable, but in this case it is the response variable. Another fun thing to do, if it doesn't happen naturally, which it often does, is to secretly ask one student to fumble the buck causing a delay and outlier for the scatter plot. Be sure to discuss the meaning of the slope and y-intercept in the context of the problem.

I have used all of these and found them to produce workable data that lead to pertinent discussions. If you need more information on how to set any of these up let me know; I'd be happy to provide additional information.

And, if you have some favorite activity for generating data for regression models and are willing to share it, I am always looking for new things to incorporate into my lessons.