Unit 6, Lesson 6
Residuals
Integrated Math 1
Preparation
Lesson Narrative
The mathematical purpose of this lesson is to informally assess the fit of a function by plotting and analyzing residuals. The term residual is introduced as the difference between the
When students take turns with a partner matching graphs of residuals to scatter plots that display linear models, students trade roles explaining their thinking and listening, which provides opportunities for them to explain their reasoning and critique the reasoning of others (MP3).
- Calculate and plot the residuals for a given data set and use the information to determine the goodness of fit for a linear model.
- Comprehend the connection between residuals, variability, and whether or not using a linear model is appropriate.
- Let’s examine how close data is to linear models.
Required Materials
Activity 2
Required Preparation
Activity 2
Acquire devices that can run Desmos (recommended) or other graphing technology. It is ideal if each student has their own device. (Desmos is available under Math Tools.)
residual
A residual is the difference between an actual data value and its value predicted by a model. It can be found by subtracting the
On a scatter plot, the residual can be seen as the vertical distance between a data point and the best-fit line.
The lengths of the dashed segments on this scatter plot show the residuals for each data point.
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