Do more selective colleges offer more grant aid? How does the typical net price of college compare to the sticker price? Through this visual and interactive activity, students will use real-world data to explore both those questions while building their conceptual understanding of regression. 

Let’s dive into DESMOS: OLS Regression and College Costs from the Financial Algebra course!

Part 1: Sticker Price and Net Price

First, students look at a scatterplot of the net price and sticker price for 15 US colleges. This small data set will make it easy for students to visualize the regression process; however, it is a decent representation of 4-year colleges across the country based on data from NCES.

Next, students estimate the line of best fit for the data set. On the following screen, they see the r² value for their line and can toggle a button to show the squared residuals visually. 

Then, they can click the “regress it!” button to see their line move to become the line of best fit. This allows students to visualize the relationship between the line, the r² value, and the squared residuals.

Part 2: Acceptance Rate and Grant Aid

Once students have built familiarity with Desmos and OLS regression, they move to another data set: acceptance rate and average student grant aid. Again, students find the line of best fit for the data set but this time, they can use the r² value and residuals to help them.

Then, students dive into analysis - they explain why their line is a good fit, analyze what would happen if the outlier was removed, and consider other types of functions that might be a better fit.

Through this Desmos activity, students intuitively experiment with lines of best fit and use visual feedback to strengthen their understanding of r².

We hope you enjoyed this activity! You can find this and more in the NGPF Financial Algebra Desmos Collection.

About the Author

Kathryn Dawson

Kathryn (she/her) is excited to join the NGPF team after 9 years of experience in education as a mentor, tutor, and special education teacher. She is a graduate of Cornell University with a degree in policy analysis and management and has a master's degree in education from Brooklyn College. Kathryn is looking forward to bringing her passion for accessibility and educational justice into curriculum design at NGPF. During her free time, Kathryn loves embarking on cooking projects, walking around her Seattle neighborhood with her dog, or lounging in a hammock with a book.