LEAST-ABSOLUTE-DEVIATION REGRESSION
The two most popular linear regression methods for estimating model coefficients are referred to as ordinary-least-squares (OLS) and least-absolute-deviation (LAD) goodness of fit, respectively. Because they are popular, a wide selection of computer software is available to help us do the calculations.
With least-squares goodness of fit, we seek to minimize the sum
where Yi denotes the variable we wish to predict and Xi the corresponding value of the predictor on the ith occasion. With the LAD method, we seek to minimize the sum of the absolute deviations between the observed and the predicted value:
Those who have taken calculus know the OLS minimum is obtained when
that is, when
and
Least-absolute-deviation regression (LAD) attempts to correct one of the major flaws of OLS, that of sometimes giving excessive weight to extreme values. The LAD method solves for those values of the coefficients in the regression equation for which the sum of the ...
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