The Ubiquity of Statistics

The use of biased estimation in data analysis and model building is discussed. A review of the theory of ridge regression and its relation to generalized inverse regression is presented along with the results of a simulation experiment and three examples of the use of ridge regression in practice. Comments on variable selection procedures, model validation, and ridge and generalized inverse regression computation procedures are included. The examples studied here show that when the predictor variables are highly correlated, ridge regression produces coefficients which predict and extrapolate better than least squares and is a safe procedure for selecting variables.