What OLS Regression Actually Does

Lesson notes

Key points

• A simple regression models an outcome Y, like household spending, as a straight-line function of one variable X, like income.
• Each observed point sits some distance from the line, and that vertical gap is called the residual.
• Ordinary Least Squares, or OLS, picks the intercept and slope that minimise the sum of squared residuals.
• The slope estimate then tells you how much Y changes, on average, when X rises by one unit.

Definitions

OLS

Estimator choosing β̂₀ and β̂₁ to minimise Σ(Yᵢ − β̂₀ − β̂₁Xᵢ)²

Takeaway: OLS fits the line minimising the sum of squared residuals.

Regression modelResidualOrdinary Least SquaresSlope interpretation