White's test

White's test for heteroskedasticity regresses squared OLS residuals on predictors, their squares, and cross-products, requiring no functional form assumption for the variance.

ByHoang TruongUpdated July 3, 2026

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White's test runs in five steps: estimate the original OLS model and keep its residuals; square them; regress the squared residuals on every predictor, their squares, and all cross-products; compute W as n times that auxiliary regression's R²; then compare W to a chi-square distribution whose degrees of freedom equal the number of auxiliary terms — nine, with three predictors.

Where it fits

SubjectData Analysis & StatisticsAdvancedTopicRegression Diagnostics & ProblemsAdvanced

The formula

LaTeX

W = n \cdot R^2_{\text{aux}} \sim \chi^2(m)

Variables

$W$: White's test statistic (dimensionless)
$n$: number of observations (dimensionless)
$R_{a}^{2} ux$: R-squared from the expanded auxiliary regression of ê² on all predictors, their squares, and cross-products (dimensionless)
$m$: number of terms in the auxiliary regression (k predictors + k squares + k(k−1)/2 cross-products) (dimensionless)

White's test assumes no functional form for the variance; degrees of freedom m grow as k(k+3)/2, reducing power in small samples compared with the Breusch-Pagan test.