AbstractThis paper provides an examination of the problem of heteroscedasticity as it relates to estimating park use, although the results can also be applied to a wide variety of flow problems involving traffic, people or commodities. The major issue is that estimates of flows obtained using ordinary least squares,OLS, often yield statistically significant results while still giving rise to large differences between observed and predicted flows (residuals).The paper presents results which show that for the flow estimation problem of concern, more accurate use estimates may be obtained by using generalized least squares,GLS, rather than usingOLS.Weights to use inGLSregression are developed taking into account the variance to be expected in origin‐destination flows.It is shown that deriving the correct weights, estimates of variances, to use in a regression analysis results in an ‘absolute’ test for the structural appropriateness of the regression model. Tests related to the ‘absolute’ adequacy test are introduced and their use to identify specific structural problems with a model is il