SWBAT create a residual plot for data based on a best fit line. Students will be able to assess the strength of the fit of a line by analyzing the residuals.

The residual plot for a regression can help students determine if the right model was used and the strength of correlation.

This Resource Video is for you, the teacher, although it could certainly be used with your students as well. The purpose of this lesson if to ensure students are comfortable with creating residual plots on their calculator. I also want to ensure that they can confidently switch between creating scatterplots, linear residual plots and exponential residual plots*.

*NOTE: The graphing calculator will create a residual plot based on the most recent regression that was calculated. The accompanying worksheet is structured in a very specific way to demonstrate this to students. It is important that you let them know that in order to create a linear residual plot they must first calculate a linear regression on their data. The same applies for calculating an exponential residual plot.

10 minutes

The direct instruction portion (residual_plots_day2_direct) of this lesson will require you to go slowly so that students are comfortable with the various keystrokes they need to make on the graphing calculator. It is strongly encouraged that you use some sort of demonstration software (TI Presenter, TI Smartview, or an overhead calculator). Because this portion of the lesson will involve a lot of teacher modeling, it is important to check for understanding along the way. I try to consistently ask questions of my students like:

- How will I calculate the linear regression?
- How do I find the residual plot?
- How can I adjust my window so that I can see the entire plot?

I have also found that letting a student use the calculator that will be displayed is a great option. This way, you are free to move around the room and monitor students progress and check in to make sure they are following along with the various steps.

Once students have had an opportunity to "gather their data" in steps a-e. I ask them to analyze their data (residual plots and correlation coefficients) to determine which model is the best fit (MP7). I then have do a brief turn and talk with their partner to determine what they are going to write. This time to "rehearse" helps students fine tune their rationale and reasoning. I want students to use both the correlation coefficient and the residual plot to make their decision. Students should try to reference both in their written answer (MP3).

As a class, we will go through Example 2 together. This time, we can move a little more quickly due to the fact that students are more familiar with the various steps and keystrokes. This will be a good time to point out to students that in order to create a linear residual plot they must first do a linear regression (the same goes for exponential regression).

25 minutes

This lesson is all about taking advantage of repetition. The residual_plots_day2_practice worksheet follows the same structure for each question because I want students to develop a comfort level with each aspect of the question. For questions 3 and 4, I let students work with their partners and I facilitate their work and give them hints or ask questions if they get stuck.

I also use this as a time to ask questions that deepen students conceptual understanding about the content. Some of these questions include:

- What does this correlation coefficient tell you about the fit of your regression equation?
- Based on that residual plot, is the linear regression a good fit?
- Looking at your scatter plot, can you anticipate which model will work best?

Encourage students to use appropriate mathematical terminology when responding to questions like this. The more comfortable they are with vocabulary the more depth and specificity they can add to their explanations (MP3).

5 minutes

This ticket out (residuals_day2_TOD) will give you immediate feedback on how well students are understanding the concept of residual plots and correlation coefficients. I really like the choices in this task because they all connect to students misunderstandings. I also ask students to explain their choice so that I can get a sense of their understanding of the concepts through their writing.