In a linear regression model, a test of the null hypothesis of homoscedasticity against the alternative hypothesis that the variance of observation i has the form ${\sigma }_i^2=h(z_i\prime \alpha ),$ where h is a function common for all i, z_i is an (S × 1) non-stochastic vector with first element equal to one, and α‎ is an (S × 1) vector of unknown coefficients. The test can be conveniently performed by (1) estimating the original regression by ordinary least squares (OLS) and (2) regressing squared OLS residuals on Z = (z₁,…,z_N). The test statistic is η‎ = NR², where N is the sample size and R² is the coefficient of determination from the second regression. Under the null hypothesis, η‎ has asymptotically chi-square distribution with (S−1) degrees of freedom; this result does not depend on the function h.