Weighted Least Squares (in Regression)

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 that 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 Examples section of Nonlinear Regression.

For more information on options for using case weights, see also Selecting a Weighting Variable.