Lesson 7: 3.7 Assessing a Regression Model

If a scatterplot looks linear, why do we still need to look at a residual plot?

What does it mean if r^2 = 0.85? (What is the "85%" referring to?)

Residual plot

Standard deviation of the residuals

Coefficient of determination

HSS-ID.A.2: Interpret differences in shape, center, and spread... accounting for possible effects of extreme data points.

The SAT expects students to know that a "pattern" in the residuals means a linear model is not a good fit. They also test the conceptual understanding of r^2 as a measure of how well the model explains the data.

Students learn that r isn't the only way to judge a line. They learn to look for a "leftover" pattern in residuals and to quantify the "average error".

The Problem: A model predicting gas mileage has s = 2.4 mpg and r^2 = 0.64.

Task: Interpret both of these values in the context of the problem.

r vs r^2

Random is good: Students often think a "messy" residual plot is bad. In this case, messy is good—it means there’s no hidden pattern the line missed.

Support: Create a "Good Fit/Bad Fit" sorting game with various scatterplots and their matching residual plots.

Extension: Have students investigate why r^2 is exactly the square of the correlation coefficient r.

Teacher assigns examples from the textbook and other resources.

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