Ordinary Least Squares (OLS) Regression
Ordinary Least Squares Regression · Also known as: ordinary least squares, classical linear regression, linear regression, en küçük kareler regresyonu
Ordinary Least Squares is the classical linear regression method that explains a continuous outcome as a linear combination of predictors. It estimates the coefficients by minimising the sum of squared residuals, and under the Gauss-Markov assumptions these estimates are the best linear unbiased estimator (BLUE).
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When to use it
OLS is a good fit when the outcome is continuous and the relationship is approximately linear in the parameters, with a reasonable sample size (at least about 30 observations). It is most reliable when the Gauss-Markov assumptions hold: linearity in the parameters, exogenous regressors that are uncorrelated with the error term, errors with no autocorrelation, predictors that are not strongly collinear, and a constant (homoscedastic) error variance. When these conditions are met OLS gives unbiased, efficient, and directly interpretable coefficients. It is less suitable for small samples, strongly collinear predictors, or non-constant error variance.
Strengths & limitations
- Best linear unbiased estimator (BLUE) under the Gauss-Markov assumptions.
- Simple, fast, and computed in one closed-form step.
- Produces directly interpretable coefficients: each βⱼ is the expected change in y for a one-unit increase in xⱼ, holding the other predictors constant.
- Coefficients become unstable and standard errors inflate in small samples (n < 30).
- Multicollinearity (VIF > 10) and heteroscedasticity invalidate the standard errors, making the t and F tests misleading.
- Assumes a linear relationship and exogenous, well-behaved errors; violations bias inference.
Frequently asked
What does R² mean in OLS?
R² is the proportion of the variance in the outcome explained by the model. Because plain R² always rises when predictors are added, judge overall fit with adjusted R² and the F-test instead.
What is heteroscedasticity and why does it matter?
Heteroscedasticity means the error variance is not constant across observations, violating a Gauss-Markov assumption. It does not bias the coefficients but invalidates the standard errors, so the t and F tests become misleading. A Breusch-Pagan test detects it; robust standard errors or quantile regression are remedies.
How do I detect multicollinearity?
Compute the variance inflation factor (VIF) for each predictor; a VIF above 10 signals strong collinearity. Collinear predictors inflate standard errors and make individual coefficients hard to interpret.
When should I use ridge or lasso instead of OLS?
When predictors are strongly collinear or the sample is small, OLS coefficients become unstable. Ridge regression shrinks coefficients to stabilise them, and lasso regression can also drop redundant predictors, trading a little bias for much lower variance.
Sources
- Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860
How to cite this page
ScholarGate. (2026, June 1). Ordinary Least Squares Regression. ScholarGate. https://scholargate.app/en/econometrics/ols-regression
Which method?
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