Glossary

Ordinary Least Squares (OLS)

Ordinary Least Squares (OLS) is the most widely used regression estimation method, which chooses coefficient estimates that minimise the sum of squared residuals. Under the Gauss–Markov assumptions, OLS is the Best Linear Unbiased Estimator (BLUE).

Definition

Why It Matters

OLS is the workhorse of applied econometrics and statistics. Its appeal lies in its simplicity, computational efficiency, and strong theoretical properties: under the Gauss–Markov conditions (linearity, exogeneity, homoscedasticity, no autocorrelation, and no perfect multicollinearity), OLS produces the most efficient unbiased estimates among all linear estimators. When these assumptions are violated — as they frequently are with real-world data — researchers turn to robust standard errors, generalised least squares, or instrumental variables rather than abandoning OLS altogether. Understanding OLS assumptions and diagnostics is essential for interpreting regression output correctly and recognising when alternative methods are needed.

Example

A researcher models house prices as a function of square footage, number of bedrooms, and neighbourhood quality using OLS regression. The coefficient on square footage is 150, meaning each additional square foot is associated with a £150 increase in price, holding other factors constant. A Breusch–Pagan test reveals heteroscedasticity, so the researcher switches to heteroscedasticity-consistent (HC) standard errors to obtain valid inference.

Related Terms

Software Notes

SPSS: Analyze > Regression > Linear; select dependent variable and independents; check assumptions via the Plots and Statistics dialogs
R: lm(y ~ x1 + x2, data = df) for OLS; coeftest(model, vcov = vcovHC) for robust standard errors
Stata: regress y x1 x2 for OLS; regress y x1 x2, vce(robust) for heteroscedasticity-consistent standard errors