Computational Approach - Weighted Least Squares
In some cases it is desirable to apply differential weights to the observations in a regression analysis and to compute so-called weighted least squares regression estimates. This method is commonly applied when the variances of the residuals are not constant over the range of the independent variable values. In this case, one can apply the inverse values of the variances for the residuals as weights and compute weighted least squares estimates. (In practice, these variances are usually not known; however, they are often proportional to the values of the independent variable(s), and this proportionality can be exploited to compute appropriate case weights.) Neter, Wasserman, and Kutner (1985) describe an example of such an analysis, which is also discussed in the Nonlinear Regression module Examples. To compute weighted least squares estimates, choose the desired weight variable, and then select the Weighted moments check box and N-1 option button on the Multiple Linear Regression Startup Panel.