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Linear Regression

Slope and intercept of regression line

📊Linear Regression (Slope & Intercept)

The slope and intercept of a linear regression line (ŷ = mx + b) describe the best-fit straight line through a scatter of data points, minimising the sum of squared vertical residuals (OLS).

  1. 1m = Σ(xi−x̄)(yi−ȳ) / Σ(xi−x̄)²
  2. 2b = ȳ − m × x̄
  3. 3Slope m has units of y/x
  4. 4Use for prediction: plug x into equation to get ŷ
Height vs weight → slope = 0.65 kg/cm=Each cm of height adds 0.65 kg to predicted weightSlope interpretation depends on units

Fun Fact

Francis Galton coined 'regression' in 1886 after noticing tall parents' children tend to be shorter — regression toward the mean is a statistical phenomenon, not a biological one.

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