In research, data sets often occur in which the variance of the distribution of the dependent variable at given levels of the predictors is a function of the values of the predictors. In this situation, the use of weighted least-squares (WLS) or techniques is required. Weights suitable for use in a WLS regression analysis must be estimated. A variety of techniques have been proposed for the empirical selection of weights with the ultimate objective being a better "fit." The outcomes of the analysis must be interpreted once the fitting is complete. Problems can arise in the interpretation of some of the statistics when using a computer package. In this paper, such problems in the application and interpretation of WLS regression using the SPSS statistical package are demonstrated, both algebraically and by example. For the purposes of the example, an artificial data set (whose underlying parametric structure is known) has been created. Each of the statistics commonly reported in the WLS regression analysis of such a data set are isolated and their interpretation discussed. Where necessary, adjusted statistics that more reasonably represent the outcomes of the analysis are proposed and their use illustrated. (BAE)