An implicit assumption underlying least squares estimation procedure is that the unknown coefficients remain invariant over sample observations. In actual practice, however, one tends to use larger and larger number of observations without verifying as to whether this assumption holds true for the entire set of sample observations. Present article examines the consequence of ignoring this fact under the framework of a general linear regression model. We find that in the presence of parametric shift within the sample, the least squares estimators are biased as well as inefficient and that the explanatory power of the model is reduced. Theoretical findings are supported by empirical evidence.