Least-Squares Regression Line — ŷ = a + bx

Slope b = r·(sᵧ/sₓ). y-intercept a = ȳ − b·x̄. The LSRL minimizes the sum of squared residuals.

StatisticsCommon Core DAT-1.BREGVerified correct ✓

Worked examples

A linear regression was computed relating study hours (x) and exam score (y). Summary statistics: x̄ = 60, ȳ = 185, sₓ = 8, sᵧ = 12, r = 0.9. The slope is b = 1.3500. Compute the y-intercept a = ȳ − b·x̄ of the least-squares regression line. Round to four decimal places.
Answer: 104

A study found a regression line relating temperature (°F) (x) and ice cream sales ($) (y): ŷ = -69.12 + 5.6250x. Use this line to predict the value of y when x = 44. Round to two decimal places.
Answer: 178.375

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Least-Squares Regression Line — ŷ = a + bx

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