Least-Squares Regression Line – AP Statistics | ShowMeClass

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Least-Squares Regression

AP Statistics · Unit 3: Collecting Data

Learning Objectives

Find and interpret slope and y-intercept of LSRL

Calculate and interpret residuals

Use r² to assess model fit

Identify influential points and outliers

LSRL Formulas

Residual

LSRL minimizes the sum of squared residuals. A residual plot should show no pattern (random scatter = good model).

LSRLRegressionResidualsAP Stats

Scatter + LSRL

Residual Plot

Sample size n 25

True slope β 1.20

Noise σ 2.0

Show residuals Highlight influential (add outlier)

Predict ŷ at x = —

Slope b—

Intercept a—

r—

r²—

SE(b)—

LSRL—

📝 Quick Quiz▼

1. The LSRL minimizes the sum of:

Residuals Squared residuals Absolute residuals Squared fitted values

2. A residual of −3 for a point means the actual y value is:

3 above ŷ 3 below ŷ Equal to ŷ The slope is 3

3. LSRL slope b = r × (sᵧ/sₓ). If r = 0.8, sᵧ = 5, sₓ = 2, then b =

0.32 8.0 2.0 0.5