# White test

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In statistics, the White test, named after Halbert White, is a test that establishes whether the residual variance of a variable in a regression model is constant (homoscedasticity). To test for constant variance one regresses the squared residuals from a regression model onto the regressors, the cross-products of the regressors and the squared regressors. One then inspects the $R^{2}$. If homoskedasticity is rejected one can use a GARCH model.

An interesting fact is that the paper that published White's test, "A Heteroskedasticity—Consistent Covariance Matrix Estimator and a Direct Test for Hetereoskedasticity” (1980) is the one of the most cited articles in Economics journals [1].

The LM test statistic is the product of the $R^{2}$ value and sample size. It follows a chi square distribution, with degrees of freedom equal to one less than the number of independent variables.

$\ LM = n \cdot R^2$