Run a Breusch-Pagan test for heteroskedasticity

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After fitting a regression on n = 200 observations with 3 explanatory variables, you save the OLS residuals, square them, and regress those squared residuals on the same 3 explanatory variables. That auxiliary regression has R^2 = 0.08. Compute the Breusch-Pagan test statistic and decide, at the 5 percent level, whether the errors are heteroskedastic.

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The idea of the test. Under constant variance (homoskedasticity), the squared residuals should not be predictable from the regressors. So we regress the squared residuals on the regressors and ask whether that auxiliary regression explains anything. If it does, the error variance moves with the regressors, which is heteroskedasticity. The statistic. The Lagrange-multiplier form of the Breusch-Pagan test is 	ext{LM} = n \cdot R^2{	ext{aux}}, where R^2{	ext{aux}} is the R^2 of the auxiliary regression. Under the null of homoskedasticity it follows a chi-square distribution with degrees of fr…

Run a Breusch-Pagan test for heteroskedasticity

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