Illuminating Statistical Analysis Using Scenarios and Simulations

54Brief on Robust Regression

Rather than transforming the data, we could transform certain aspects of the statistical analysis method. For example, what would happen if we transformed the “least-squares” criteria in least-squares linear regression into a “least absolute value” criteria instead?

Instead of this (Chapter 41)

we have this

The impact of outliers would certainly be reduced. Recall that squaring the deviations between the actual and predicted values for is what made outliers so extra troublesome for least-squares linear regression because least-squares regression fits the regression equation to minimize the squared deviations. If we used the absolute value of the deviations instead, the impact of outliers would be less severe.

This is the type of thing that is done by robust regression methods. Do an online search for “robust regression”. A related topic is “generalized linear models”.