Linear and Exponential Regression

It’s that time of year when seniors are receiving their college acceptance letters. Woohoo, so exciting! The school where I work is very small, so we acknowledge each acceptance for every senior at monthly assemblies. It’s so neat to hear all the different schools that our students have been accepted! Often I get a little teary-eyed because I am so proud of them.

This makes it a perfect time for me to whip out the College Trend Project involving linear and exponential lines of best fit. Students research different universities to see if the tuition is trending as a linear or exponential function and predict future tuition costs.

So, if you are looking for a “real world” project that is engaging and meaningful, look no further!

The College Trend Project – Real World Linear and Exponential Regression

Objectives

Students will be able to demonstrate their knowledge and understanding of the following skills:

• Gather accurate data and create a table
• Graph a scatter plot
• Find the linear and exponential line of best fit and graph
• Determine which equation (linear or exponential) best models the data
• Predict future tuition costs using the line of best fit function
• Research background information about each university/college

The Data Hunt

Students start by collecting real-world data on college tuition. Why gather this data themselves, you ask? Well, first, it makes the project more engaging because they’re investigating something that directly impacts their lives and future. Second, it ensures they don’t just copy information from a website without thinking about it. Students take the time to research multiple colleges or universities, recording tuition trends over the years in an organized table. This is where they start seeing algebra in action in the real world.

The Graph

Once the data is collected, students graph a scatter plot of tuition versus year. From there, they explore three different types of regression: linear, quadratic, and exponential. Using either graphing calculators or Desmos, students find the line or curve of best fit for their data. They analyze each model using the coefficient of determination to see which equation best represents the data. This is a great way for students to see how different functions behave in real-world situations, and how math helps make predictions about the future.

The Presentation

Instead of individual presentations, students summarize their findings in a report, visual poster, or presentation. Give students a chance to learn about each university by hanging the posters up around the room or students present their colleges and results.

Grading

Like any good project, this one uses a rubric. Projects are evaluated on neatness/organization, accuracy of data collection, quality of the scatter plot, the regression equations, the analysis of which model fits best, and predictions of future tuition costs.

Student Example
Here is an example of  a College Trend Project.

Of all the projects we do, this is definitely my students’ favorite. They LOVE to research universities they are interested in attending and are shocked by how much the cost has changed over the years. I also incorporate a stations activity, so students can review each other’s projects. The students have fun looking at other universities they may not have thought of or even heard of before. Plus, these student sheets help you grade the projects too, which is a nice perk!

Most students do this project in 9th or 10th grade, so by the time they are seniors, we love to look back and talk about the schools they thought they would attend and how their plans may have changed.

If you are interested in learning more about this project and using it in your class, click HERE. The project and rubric are 100% editable, so you can adjust the years. Plus, I’ve included two bonus calculator reference sheets (linear regression and exponential regression) to help your students with the line of best fit portion of the project. Oh, and I forgot to mention there is a ton of technology integrated into this project!

Update

The project has been updated to include Quadratic Regression as well. Remember, it is 100% editable, so you can decide which regression models you want your students to evaluate.