AP Statistics · Lesson 3 of 6 · Unit 5

Linear regression models, prediction and extrapolation

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Linear regression models turn an observed linear pattern between two quantitative variables into a mathematical formula for making predictions. On the AP Statistics exam, this topic can appear in discrete multiple-choice questions, the Section I three-question set on regression analysis, and Section II (for example Question 2 or 4), where you may be asked to calculate predicted values and evaluate whether a prediction is trustworthy.

By the end you’ll be able to

Calculate a predicted response $\hat{y}=a+bx$ from a linear regression model for a given value of the explanatory variable.
Explain when a linear regression model is a reasonable way to approximate the relationship, based on its form.
Distinguish interpolation from extrapolation, and explain why predictions become less reliable the further they are extrapolated.

What the exam asks

Calculate a predicted value of the response variable () for a specific value of the explanatory variable () using a given equation or computer output.

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Symbol	Meaning
$x$	Value of the explanatory variable
$\hat{y}$	Predicted value of the response variable (read as “ $y$ -hat”)
$a$	$y$ -intercept: the predicted value of $y$ when $x = 0$
$b$	Slope: the predicted change in $y$ for each 1-unit increase in $x$

Linear regression models, prediction and extrapolation

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What the exam asks

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Still to come

Core ideas

The linear regression model

When is a linear model reasonable?