It is shown that the information contained in the incomplete portion of the sample that is relevant in the estimation of the regression parameters is in the form of a linear restriction. Although the parameters of this restriction are generally unknown they can be estimated in terms of the complete portion of the sample. It is then shown that regression parameter estimates based on first order methods, say, Ĉ, differ from the ordinary least squares estimates based only on the complete portion of the sample, say ĈLS, by a function of the extent to which ĈLSfails to satisfy the above named restriction. The asymptotic variance-co-variance matrix of Ĉ is derived under various conditions and compared to that of ĈLS.