Lesson 5: 3.5 Regression Lines
Duration of Days: 3
Lesson Objective
Students will be able to interpret the slope and y-intercept of a regression line in context and use the equation to make predictions (including identifying the dangers of extrapolation).
If the slope of a line is 5, what does that actually tell us about the relationship between our x and y variables?
Why is it "illegal" in statistics to predict the height of a 40-year-old using a growth model built for toddlers?
Regression line
Predicted value
Slope
y-intercept
Extrapolation
HSS-ID.B.6.A: Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
This is one of the most common SAT Math topics. Students are frequently given a scatterplot with a line of best fit and asked to "Interpret the meaning of the slope".
This section introduces the line as a predictive model. Students learn the anatomy of the linear equation and how to use it responsibly.
The Problem: A regression line y-hat = 32 + 0.5x relates x = study time (minutes) to y = test score.
Task: Interpret the slope and the y-intercept. If a student studies for 200 minutes, what is their predicted score? Why might we be cautious of this prediction?
y vs y-hat
Slope interpretation
Support: Provide a "Sentence Starter" template for interpreting slope.
Extension: Have students find a y-intercept that is statistically significant but contextually nonsensical.
Teacher assigns examples from the textbook and other resources.
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