AP®︎ Statistics (pre-2026): Topic 2.8 Flashcards

Master key terms and definitions for Topic 2.8 of AP Statistics (pre-2026) – Least Squares Regression to help you prep for quizzes and the AP exam.

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Term

Least Squares Regression Line (LSRL)

Definition

The line y-hat = a + bx that minimizes the sum of squared residuals.

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Least Squares Regression Line (LSRL)
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The line y-hat = a + bx that minimizes the sum of squared residuals.

DAT-1.GDAT-1.G.1
Residuals and Why They Are Squared
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Residuals are observed minus predicted values; squaring prevents cancellation and emphasizes larger errors.

DAT-1.GDAT-1.G.1
LSRL Form
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Predicted response equals y-hat = a + bx, with a as intercept and b as slope.

DAT-1.HDAT-1.H.1
Slope of the LSRL
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The predicted change in y for each 1-unit increase in x.

DAT-1.HDAT-1.H.2
Slope Formula
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Compute slope with b = r(sy/sx), using correlation and the variables' standard deviations.

DAT-1.GDAT-1.G.2
Y-Intercept Formula
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Compute intercept with a = y-bar - b x-bar.

DAT-1.HDAT-1.H.3
LSRL Passes Through (x-bar, y-bar)
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The regression line always contains the point of the sample means.

DAT-1.GDAT-1.G.1
Coefficient of Determination / r-squared
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The square of r; the proportion of y-variation explained by its linear relationship with x.

DAT-1.GDAT-1.G.4
Interpreting r-squared
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State the percent of variation in the response variable explained by the linear model with x.

DAT-1.GDAT-1.G.4
Y-Intercept of the LSRL
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The predicted y-value when x = 0, though it may lack meaning in context.

DAT-1.HDAT-1.H.3