 # Analyzing Residuals

Related Topics:
Lesson Plans and Worksheets for Algebra I
Lesson Plans and Worksheets for all Grades
More Lessons for Algebra I
Common Core For Algebra I

Videos and lessons with examples and solutions to help Algebra I students learn to use a graphing calculator to construct the residual plot for a given data set.

Students use a residual plot as an indication of whether the model used to describe the relationship between two numerical variables is an appropriate choice.

### New York State Common Core Math Algebra I, Module 2, Lesson 17, Lesson 18

Worksheets for Algebra I, Module 2, Lesson 17 (pdf)
Worksheets for Algebra I, Module 2, Lesson 18 (pdf)

In these lessons, students use technology to generate residual plots. Students build on their knowledge of using technology to determine the least-squares line for a data set.

Lesson 17 Summary

After fitting a line, the residual plot can be constructed using a graphing calculator.

A pattern in the residual plot indicates that the relationship in the original data set is not linear.

Example 3

In an earlier lesson you looked at a data set giving the shoe lengths and heights of 12 adult women. This data set is shown in the table below.
Use a calculator to construct the scatter plot (with least-squares line) and the residual plot for this data set.

Lesson 17 Exit Ticket

1. If you see a random scatter of points in the residual plot, what does this say about the original data set?

2. Suppose a scatter plot of bivariate numerical data shows a linear pattern. Describe what you think the residual plot would look like. Explain why you think this. Using the TI-84 Calculator.

Using the TI-Nspire Calculator.

Lesson 18 Summary
• After fitting a line, the residual plot can be constructed using a graphing calculator.
• A curve or pattern in the residual plot indicates a curved (nonlinear) relationship in the original data set.
• A random scatter of points in the residual plot indicates a linear relationship in the original data set.

Lesson 18 Exit Ticket

1. If you see a clear curve in the residual plot, what does this say about the original data set?

2. If you see a random scatter of points in the residual plot, what does this say about the original data set?

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 