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Ridge regression in two‐parameter solution
Author(s) -
Lipovetsky Stan,
Conklin W. Michael
Publication year - 2005
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.603
Subject(s) - multicollinearity , orthogonality , ridge , regression , generalization , mathematics , elastic net regularization , regression analysis , interpretation (philosophy) , statistics , computer science , geology , mathematical analysis , geometry , paleontology , programming language
We consider simultaneous minimization of the model errors, deviations from orthogonality between regressors and errors, and deviations from other desired properties of the solution. This approach corresponds to a regularized objective that produces a consistent solution not prone to multicollinearity. We obtain a generalization of the ridge regression to two‐parameter model that always outperforms a regular one‐parameter ridge by better approximation, and has good properties of orthogonality between residuals and predicted values of the dependent variable. The results are very convenient for the analysis and interpretation of the regression. Numerical runs prove that this technique works very well. The examples are considered for marketing research problems. Copyright © 2005 John Wiley & Sons, Ltd.