##
* *Reflection: Developing a Conceptual Understanding
Creating a Residual Plot - Section 4: Closure

This entire lesson basically focused on two measures to determine the strength of fit of a regression model. The exit ticket was aligned to that goal and gave me instant feedback on what students were understanding about correlation coefficients and residual plots. The results from this exit ticket showed students had a strong understanding of what they were looking for in these different representations (see attached student work).

The one change that I would make to this closing in the future is to extend the task slightly. I asked students to answer the question and explain their choice. In the future, I would ask them to explain why the other choices showed a strong linear correlation. Adding this dimension to the questions would require students to confront their misconceptions (for example, that -0.93 shows a poor fit) and explain each of the choices rather than one of them. I feel like this would give me even better data on student understanding.

*Developing a Conceptual Understanding: Analyzing Multiple Representations*

# Creating a Residual Plot

Lesson 18 of 19

## Objective: 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.

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.

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#### Direct Instruction

*10 min*

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).

*expand content*

#### Guided Practice

*25 min*

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).

#### Resources

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#### Closure

*5 min*

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.

#### Resources

*expand content*

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- LESSON 1: Asking a Statistical Question
- LESSON 2: Measures of Center
- LESSON 3: Practice with Measures of Central Tendency
- LESSON 4: Organizing Data with a Box Plot
- LESSON 5: Understanding Box Plots (with Assessment)
- LESSON 6: Analyzing a Box Plot
- LESSON 7: Constructing a Histogram
- LESSON 8: Modeling with Box Plots and Histograms
- LESSON 9: Connecting Box Plots and Histograms
- LESSON 10: What's this table saying?
- LESSON 11: Creating Two-Way Tables
- LESSON 12: More with Conditional, Joint, and Marginal Frequencies
- LESSON 13: Using a Scatterplot to Model Data
- LESSON 14: A Bivariate Relationship
- LESSON 15: Scatterplots and Non-Linear Data
- LESSON 16: Modeling with Non-Linear Data
- LESSON 17: Analyzing Residuals
- LESSON 18: Creating a Residual Plot
- LESSON 19: Got Ups? A Statistics Unit Task