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A Good Enough Fit?

Estimated Time: 60-75 minutes

Lesson Objectives:

  • Students will review linear regression and analyze how well the model fits the data.
  • Students will be introduced to residuals and the correlation coefficient and use these tools to determine whether or not a linear model is the best fit for a data set.

Resources for this lesson:

Before you begin, download your Algebra II Journal opens in new window for A Good Enough Fit? You will be completing activities in the journal throughout this lesson.

Visit this section on each page to access information about key terms and other resources to help facilitate the lesson.

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> Teacher Resources: Instructional Notes opens in new window

Key Common Core State Standards:

S.ID.6 Represent data on two quantitative variables on a scatter plot and describe how the variables are related.

  1. Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
  2. Informally assess the fit of a function by plotting and analyzing residuals.
  3. Fit a linear function for a scatter plot that suggests a linear association.

S.ID.7 Interpret the slope (rate of change) and intercept (constant term) of a linear model in the context of the data.

S.ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.

Supporting Common Core State Standards:

F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. 

F.LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.

Standards for Mathematical Practices:

MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.

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