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We consider the standard linear regression model y=Xβ+u with all standard assumptions, except that the variance matrix is assumed to be σ ²Ω(θ) , where Ω depends on m unknown parameters θ ₁,…, θ _m. Our interest lies exclusively in the mean parameters β or Xβ. We introduce a new sensitivity statistic (B1) which is designed to decide whether ŷ (or β ̂ ) is sensitive to covariance misspecification. We show that the Durbin–Watson test is inappropriate in this context, because it measures the sensitivity of σ ̂ ² to covariance misspecification. Our results demonstrate that the estimator β ̂ and the predictor ŷ are not very sensitive to covariance misspecification. The statistic is easy to use and performs well even in cases where it is not strictly applicable.