In a multiple regression model the residual variance is an unknown function of the explanatory variables, and estimated by nearest neighbor nonparametric regression. The resulting weighted least squares estimator of the regression coefficients is shown to be adaptive, in the sense of having the same asymptotic distribution, to first order, as estimators based on knowledge of the actual variance function or a finite parameterization of it. A similar result was established by Carroll (1982) using kernel estimation and under substantially more restrictive conditions on the data generating process than ours. Extensions to various other models seem to be possible.