Analyzing ResidualsGrade 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.

Launch

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y

What will the residual plot look like?

x

y

0x

Res

idua

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Why is looking at the pattern in the residual plot important?

Calculating Residuals and Constructing a Residual PlotDestination Distance (miles) Airfare ($)

Atlanta 576 178

Boston 370 138

Chicago 612 94

Dallas/Fort Worth 1216 278

Detroit 409 158

Denver 1502 258

Miami 946 198

New Orleans 998 188

New York 189 98

Orlando 787 179

Pittsburgh 210 138

St. Louis 737 98

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?

Why is it important to look at the residual plot?

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

› S.ID-6b: Informally assess the fit of a function by plotting and analyzing residuals.

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.