AP Statistics — regression from computer output

This material trains Unit 5 of the AP Statistics course framework for 2026–27, Regression Analysis, with the emphasis the revised course puts on it: the least-squares line is computed with technology, and the skill is reading and interpreting what the technology reports. On the exam this unit appears in single multiple-choice questions, in a multiple-choice set built on one scenario, and in part of a free-response question. The material is written at introductory college level.

Several quiz questions share one piece of computer output, as a multiple-choice set would: a regression of used-car price on age. From it you write the equation of the line, interpret the slope as a predicted change, find the correlation from R-Sq with the sign of the slope, compute a prediction and a residual and say whether the line under- or overpredicts, interpret $r^{2}$ as the proportion of variation explained, judge the intercept as an extrapolation, and find how far apart the predictions for two ages are. Other questions ask you to give a complete description of a scatterplot (form, direction, strength, unusual features), find the intercept from the point of means, recognize that a correlation near 1 does not rescue a curved residual plot, put the explanatory and response variables on the right axes, and make and classify a prediction from a second output. Every explanation shows the arithmetic and why each wrong answer fails.

The flashcards review how to read output, the least-squares line and the point of means, the interpretations of slope, intercept, residual and $r^{2}$ , residual plots, and interpolation versus extrapolation.

The written work is a printable sheet of eight free-response tasks: a complete analysis of a regression output, describing a curved scatterplot, what residual plots show, predictions and extrapolation for house prices, correlation and a confounding variable, a least-squares line computed with technology from six data points, how units, switching variables and unusual points affect $r$ , and the meaning of R-Sq. Handwritten answers are photographed and checked against model answers and key points.

The oral exam has an examiner read regression output aloud and ask one question at a time, from the equation to residuals and the limits of the model, closing with short, precise feedback.

Inference for slopes, influential points and transformations are no longer part of the 2026–27 framework and are not included. All scenarios are invented and all questions are original practice items written by Zestly, not released exam questions. The material follows the published course framework but is independent practice and does not predict an exam score.

Read the intercept, slope and R-Sq from regression output and write the least-squares equation in context
Interpret the slope and y-intercept in context and recognize when the intercept is an extrapolation
Find the correlation from R-Sq and the sign of the slope, and interpret $r^2$
Compute predictions and residuals and say whether the model over- or underpredicts
Describe a scatterplot by form, direction, strength and unusual features, and judge a linear model from a residual plot
Distinguish interpolation from extrapolation and association from causation

Practice material written by Zestly, based on the College Board AP Statistics course framework effective fall 2026 (Unit 5, Regression Analysis, topics 5.1–5.5). Original questions, not released exam items.

Sample question

A dealer fits a least-squares line to predict the price (in thousands of dollars) of 25 used cars of one model from their age (in years); the ages in the data run from 1 to 12 years. Computer output: Constant, coefficient 28.40; Age, coefficient -2.15; R-Sq = 81.0%. What is the equation of the least-squares regression line?

$\widehat{\text{age}} = 28.40 - 2.15(\text{price})$
$\widehat{\text{price}} = 28.40 - 2.15(\text{age})$
$\widehat{\text{price}} = -2.15 + 28.40(\text{age})$
$\widehat{\text{price}} = 28.40 - 0.81(\text{age})$

See the answer

$\widehat{\text{price}} = 28.40 - 2.15(\text{age})$

In regression output the 'Constant' row gives the y-intercept and the row labeled with the explanatory variable (Age) gives the slope, so predicted price $= 28.40 - 2.15 \times$ age. The response is price, not age; swapping the two coefficients puts the intercept in the slope's place; and 0.81 is $r^2$, not a coefficient.

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