With Laura Ziegler and Anna Peterson (Iowa State University)
We propose an activity for having students explore simple linear regression models for different types of building bricks including Legos and Mega Bloks. In a traditional setting, multiple regression is introduced with two quantitative explanatory variables (e.g., (Moore, McCabe, Alwan, & Craig, 2015), (Cannon, et al., 2013)). This can make it difficult for students to visualize what actually happens when the second explanatory variable is added. Over many semesters teaching students in a transition from simple linear regression to multiple regression we have observed anecdotally that students struggle adding a second quantitative explanatory variable to a model. The GAISE College Report (GAISE, 2016) encourages the use of meaningful graphs with multivariate data and provides an example of a scatterplot with simple linear regression lines for multiple categories of a qualitative variable. The example scatterplot illustrates that students can look at results in a scatterplot involving more than two variables before being introduced to multiple regression. Therefore, by choosing the second variable to be qualitative, students can play with the data and build their understanding of multiple regression modeling aided by visualization.
To investigate the potential of using graphs to introduce multiple regression using qualitative and quantitative variables, we developed a new activity where students create their own multiple regression model. The goal was for students to discover the transition from simple linear regression to multiple regression. The activity was designed to be used in a 2 hour lab with 40-50 students working in established cooperative groups with a variety of majors where students have access to JMP Pro 12. Using cooperative groups to learn about relationships promotes active learning as recommended in the GAISE College Report (GAISE, 2016).
In our activity, students fit simple linear regression models to predict price by number of pieces per set for two types of Legos; City Legos and Friends Legos. Students utilized Graph Builder in JMP which allows students to drag their variables to the appropriate axes as well as to color the points based on Lego type to visualize and discuss their differences. Students included the simple linear regression lines on the plot separately for each type and saw similar slopes. Students started with an assumption that the slopes were identical. Students were told to start with the simple linear regression model for one type of Lego and expand it to allow for different intercepts. We provided guidance to students, students struggled through, and we were excited that most student groups were able to figure out how to create the model.
The second half of the activity, students were asked to describe the relationship between price and number of pieces for Legos and their competition, Mega Bloks. With these groups, the slopes are not similar. Once again, they started by building their graph and added their simple linear regression lines. Students were guided on how to fit the multiple regression model including an interaction term using JMP.
Our poster will provide highlights of the activity, discuss student responses, and provide suggestions on how to implement the activity. Overall the students were engaged in the lab. While this was not a formal research study, our anecdotal impressions were very positive. Students seemed to understand the need for adding an interaction term in the model in the second half of the activity. After the activity, it was easy to motivate the use of two quantitative explanatory variables in multiple regression and it was straightforward to discuss what the coefficients represented.