Breusch-Pagan Test (BP Test)

Keith Tan, CFA


The Breusch-Pagan test is a statistical test used to detect the presence of heteroskedasticity in a linear regression model. It is based on the idea that if heteroskedasticity is present, the variance of the error term should be related to the predictor variables in the model.

The test involves regressing the squared residuals of the original regression model on the predictor variables and testing the significance of the resulting coefficients. If the coefficients are significantly different from zero, it indicates the presence of heteroskedasticity.

To perform the Breusch-Pagan test, the following steps can be followed:

  1. Fit a linear regression model to the data and obtain the residuals.
  2. Square the residuals and save them as a new variable.
  3. Regress the squared residuals on the predictor variables from the original model.
  4. Test the significance of the coefficients in the squared residual regression model.

If the p-values of the coefficients are below a certain threshold (usually 0.05), it suggests that heteroskedasticity is present in the original model.

It is worth noting that the Breusch-Pagan test is sensitive to the presence of multicollinearity in the model, so it is recommended to check for and address this issue before performing the test.

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