3.3.6 Lesson Summary

In this lesson, you learned how to:

• Plot and calculate residuals for a data set and use the information to judge whether a linear model is a good fit.

Here are the activities that helped you reach those goals:

• 3.3.1: Subtracting an Estimated Value from an Actual Value
  • In this activity, you discussed strategies and understandings you had for subtracting an estimated value from an actual value. This discussion helped you develop fluency and helped prepare you to compute residuals from a linear model.
• 3.3.2: Plotting and Analyzing Residuals
  • In this activity, you explored the concept of residuals, plotted residuals, and analyzed the residuals to informally assess the fit of a function. In this activity, you also fitted a function to data and used the function to solve problems. You learned that a residual is the difference between the actual $y$-value for a point and the expected $y$-value for the point on the linear model with the same associated $x$-value.
  • 3.3.2: Self Check
  • 3.3.2: Additional Resources
• 3.3.3: Matching Residuals Graphs to Scatter Plots
  • In this activity, you took turns with a partner, matching graphs of residuals to scatter plots that displayed linear models. You explained your thinking and listened in order to explain your reasoning and critique the reasoning of others. You recognized that a plot of the residuals for data that are fit well by a linear model shows residuals that are close to the $x$-axis and do not show a noticeable pattern.
  • 3.3.3: Self Check
  • 3.3.2: Additional Resources
• 3.3.4: Identifying Best Fit Line for Residuals on a Graph
  • In this activity, you identified a graph most likely to represent the residuals from the best fit line.

After these activities, you completed the following practice:

• 3.3.5: Practice