Breusch-Pagan test
The Breusch-Pagan test detects heteroskedasticity by regressing squared OLS residuals on the original predictors and testing whether those coefficients are jointly zero. A significant chi-square indicates non-constant error variance.
See it move
After running OLS, the Breusch-Pagan test squares the residuals and regresses them on the original predictors. The statistic BP = n × R² from that auxiliary regression follows a chi-square distribution with k degrees of freedom. A small p-value rejects homoskedasticity, meaning error variance changes systematically with a predictor, such as firm size.
The formula
Variables
- Breusch-Pagan test statistic (dimensionless)
- number of observations (dimensionless)
- R-squared from regressing squared OLS residuals on the original k predictors (dimensionless)
- number of predictors in the original regression (excluding intercept) (dimensionless)
A significant result rejects H₀ of constant error variance. Remedies include heteroskedasticity-robust standard errors, weighted least squares, or model re-specification.