Weighted regression

Method that can be used when the least squares assumption of constant variance in the residuals is violated (heteroskedasticity). With the proper weight, this procedure minimizes the sum of weighted squared residuals to produce residuals with a constant variance (homoskedasticity).

Determining the proper weight to use can be a challenging task. The ideal weight is the reciprocal of the variance of the error. However, this is generally incalculable and other methods must be used. Alternative methods include using:

·    The reciprocal of a predictor or squared predictor if the variance is proportional to a predictor. Use experience combined with trial and error to see what works.

·    Values based on theory, the literature, or prior research.

Suppose your regression model predicts the annual number of traffic accidents in different cities. Because more populous cities tend to have more accidents, the residuals for larger cities also tend to be larger. One method for resolving this is to use the reciprocal of each city's population for the weight.