Breusch-Pagan Test for Heteroscedasticity

Breusch–Pagan test (named after Trevor Breusch and Adrian Pagan) is used to test for heteroscedasticity in a linear regression model.

Assume our regression model is $Y_i = \beta_1 + \beta_2 X_{2i} + \mu_i$ i.e we have simple linear regression model, and $E(\mu_i^2)=\sigma_i^2$, where $\sigma_i^2=f(\alpha_1 + \alpha_2 Z_{2i})$

That is $\sigma_i^2$ is some function of the non-stochastic variable Z‘s. f() allows for both the linear and non-linear forms of the model. The variable Z is the independent variable X or it could represent a group of independent variables other than X.

Step to Perform Breusch-Pagan test

  1. Estimate the model by OLS and obtain the residuals $\hat{\mu}_1, \hat{\mu}_2+\cdots$
  2. Estimate the variance of the residuals i.e. $\hat{\sigma}^2=\frac{\sum e_i^2}{(n-2)}$
  3. Run the regression $\frac{e_i^2}{\hat{\sigma^2}}=\beta_1+\beta_2 Z_i + \mu_i$ and compute explained sum of squares (ESS) from this regression
  4. Test the statistical significance of ESS/2 by $\chi^2$-test with 1 df at appropriate level of significance (α).
  5. Reject the hypothesis of homoscedasticity in favour of heteroscedasticity if $\frac{ESS}{2} > \chi^2_{(1)}$ at appropriate level of α.

Note that the

  • Breusch-Pagan test is valid only if μi‘s are normally distributed.
  • For k independent variables, ESS/2 have ($\chi^2$) Chi-square distribution with k degree of freedom.
  • If the μi‘s (error term) are not normally distributed, White test is used.


Incoming search terms:

  • breusch pagan test
  • breusch pagan
  • yhs-1
  • how to tell homoscedastistic measures with breusch pagan test
  • breusch–pagan test
  • what is exclusion assumption regressions
  • bresuh pagan test in stata
  • breush-pagan test for heteroskedasticity
  • Breusch-Pagan test
  • Breusch-Pagan-Godfrey
Be Sociable, Share!

Leave a Reply

Your email address will not be published. Required fields are marked *


question razz sad evil exclaim smile redface biggrin surprised eek confused cool lol mad twisted rolleyes wink idea arrow neutral cry mrgreen

You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <strike> <strong>