AP®︎ Statistics: Topic 5.5 Flashcards

Master key terms and definitions for Topic 5.5 of AP Statistics – Least-Squares Regression to help you prep for quizzes and the AP exam.

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Term

Least-Squares Regression Line (LSRL) / Regression Line / Line of Best Fit

Definition

The line ŷ = a + bx for predicting y from x that has the smallest possible sum of squared residuals

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Least-Squares Regression Line (LSRL) / Regression Line / Line of Best Fit
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The line ŷ = a + bx for predicting y from x that has the smallest possible sum of squared residuals

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Residual
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eᵢ = yᵢ - ŷᵢ; observed response minus predicted response

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Least-Squares Criterion
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Choose the line for which the sum of squared residuals, Σeᵢ², is as small as possible

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Least-Squares Regression Equation
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ŷ = a + bx, where ŷ is the predicted response, a is the y-intercept, and b is the slope

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Slope of the LSRL
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b; the predicted increase or decrease in the response variable for a 1-unit increase in the explanatory variable

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Y-Intercept of the LSRL
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a; the predicted value of the response variable when the explanatory variable x = 0; interpret in context only if x = 0 is meaningful and relevant

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Point the LSRL Always Passes Through
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(x̄, ȳ)

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Intercept Formula from the Means
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A = ȳ - bx̄.

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Slope Formula from Correlation and Standard Deviations
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b = r(s_y/s_x)

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Correlation Coefficient
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r; a unit-free measure of the direction and strength of the linear association between x and y

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Coefficient of Determination
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r²; the proportion of variation in the response variable explained by its linear relationship with the explanatory variable

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How to Read Regression Output Coefficients
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Intercept or Constant row gives the intercept; the explanatory-variable row gives the slope; match coefficients to the displayed equation form

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Coefficients of the LSRL
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A and b; the y-intercept and slope of ŷ = a + bx

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