Analyzing Residuals: Understanding Linear Models in Grade 9
In this Grade 9 lesson, students will learn to analyze residuals and use residual plots to determine the appropriateness of linear models for given data sets. Through hands-on activities, they will create scatter plots, find least-squares regression lines, and construct corresponding residual plots. Key questions will guide their understanding of the importance of residual analysis and its implications for model fitting. Success will be measured by the ability to effectively utilize graphing calculators to visualize and interpret residuals, reinforcing the connection between mathematics and data interpretation.
Analyzing Residuals: Understanding Linear Models in Grade 9
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Presentation Transcript
Analyzing Residuals Grade 9 Lesson 17
Learning Intentions • We are learning to analyze residuals.
Success Criteria • We are successful when we can... • show a residual plot on a graphing calculator for a set of data. • use a residual plot to decide if a linear model is appropriate for the data set.
Why is looking at the pattern in the residual plot important?
Example 3 • On poster paper and using your group’s data set: • Create a scatter plot of the data. • Find the least-squares regression line and graph this line on your scatter plot. • Create the residual plot. • Be prepared to share your poster and results with the class.
Questions to think about: • Why is it important to look at the residual plot? • Which data sets can be modeled well with linear model and why? • How can you tell if a linear model is a good fit? • Should any of these be modeled by something other than a linear function? How can you tell?
Lesson 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.
Exit Ticket • Please go to m.socrative.com • Room number: 029102 • 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.
Learning Intentions • We are learning to analyze residuals.
Success Criteria • We are successful when we can... • show a residual plot on a graphing calculator for a set of data. • use a residual plot to decide if a linear model is appropriate for the data set.
Standards Content standard Practice Standard MP4: Model with mathematics. Students use residuals and residual plots to assess if a linear model is an appropriate way to summarize the relationship between two numerical variables. • S.ID-6b: Informally assess the fit of a function by plotting and analyzing residuals.
