Economists and other users of statistical methodology often posit a probabilistic model of some real world phenomenon which has more unknown parameters than there are sample observations. In such cases it is usually impossible to estimate jointly all parameters from the sample data. Even in those instances where there are well established estimation procedures when the number of sample observations, n, is than the number of parameters, r, these methods are generally inadequate when n < r, as the necessary calculations cannot be carried out. Furthermore, when n is only slightly larger than r, such estimates often prove to be unreliable in more than one sense. One particular example of such a problem that frequently occurs in analysis of psychological and economic data can be paraphrased as follows: the researcher posits a linear regression model as defined in equation (1) below with r 1 independent variables, but only n < r observations are available. Since the standard least squares procedure cannot be applied, he may ask the following seemingly reasonable question: What subset of the r 1 independent variables should I select for inclusion in a new model to which I can apply the standard least squares procedure? Our purpose here is to demonstrate that one frequently used ad hoc method for determining such a subset by ordering simple sample correlation coefficients can be highly misleading. Any procedure which uses a given set of sample data both to determine the structure of the model to be estimated and to estimate parameters of this model is intuitively unsettling. Here we present tables which quantitatively demonstrate how dangerous such ad hoc methods can be. II Ad Hoc Use of Simple Correlation Coefficients to Determine Model Structure