Breusch-Pagan Test

A Breusch-Pagan Test is a statistical test for the null hypothesis of heteroskedasticity in a linear regression model.

• See: Statistical Test, Null Hypothesis, Linear Regression, White Test.

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References

2016

• (Wikipedia, 2016) ⇒ http://en.wikipedia.org/wiki/Breusch-Pagan_test 2016-08-13
  • In statistics, the Breusch–Pagan test, developed in 1979 by Trevor Breusch and Adrian Pagan, is used to test for heteroskedasticity in a linear regression model. It was independently suggested with some extension by R. Dennis Cook and Sanford Weisberg in 1983. It tests whether the estimated variance of the residuals from a regression are dependent on the values of the independent variables. In that case, heteroskedasticity is present.

Suppose that we estimate the regression model

[math]\displaystyle{ y = \beta_0 + \beta_1 x + u, \, }[/math]

and obtain from this fitted model a set of values for [math]\displaystyle{ \hat{u} }[/math], the residuals. Ordinary least squares constrains these so that their mean is 0 and so, given the assumption that their variance does not depend on the independent variables, an estimate of this variance can be obtained from the average of the squared values of the residuals. If the assumption is not held to be true, a simple model might be that the variance is linearly related to independent variables. Such a model can be examined by regressing the squared residuals on the independent variables, using an auxiliary regression equation of the form

[math]\displaystyle{ \hat{u}^2 = \gamma_0 + \gamma_1 x + v.\, }[/math]

This is the basis of the Breusch–Pagan test. If an F-test confirms that the independent variables are jointly significant then the null hypothesis of homoskedasticity can be rejected.

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