The mathematical derivation of the statistics used for inference in some linear models assumes that the values of the independent variables are measured without error. This assumption is often disregarded when these models are utilized in research. This study is an investigation of the consequences of the violation of this assumption for one family of linear models on the magnitude of these statistics and the frequency of Type I error in these models. The results of this study indicate that although the frequency of Type I error in these models is relatively unaffected, the values of the statistics are seriously affected by the concomitant variable being other than error-free. (Author)