Journal of Statistical Theory and Applications

Volume 20, Issue 2, June 2021, Pages 242 - 250

Optimum Ridge Regression Parameter Using R-Squared of Prediction as a Criterion for Regression Analysis

Authors
Akbar Irandoukht*
Catalysis Division, Research Institute of Petroleum Industry, Tehran, 1485733111, Iran
*Corresponding author. Email: irandoukhta@ripi.ir
Corresponding Author
Akbar Irandoukht
Received 19 August 2018, Accepted 9 April 2019, Available Online 26 March 2021.
DOI
https://doi.org/10.2991/jsta.d.210322.001How to use a DOI?
Keywords
Ridge parameter; PRESS; Maximization of R2-prediction; Model prediction power
Abstract

The presence of the multicollinearity problem in the predictor data causes the variance of the ordinary linear regression coefficients to be increased so that the prediction power of the model not to be satisfied and sometimes unacceptable results be predicted. The ridge regression has been proposed as an efficient method to combat multicollinearity problem long ago. In application of ridge regression the researcher uses the ridge trace and selects a value of ridge parameter in such a manner that he thinks the regression coefficients have stabilized; this leads the ridge regression to be subjective technique. The purpose of this paper is the conversion of the ridge regression method from a qualitative method to a quantitative one meanwhile to present a method to find the optimum ridge regression parameter which maximizes the R-squared of prediction. We examined four well-known case studies on this regard. Significant improvements at all of the cases demonstrated the validity of our proposed method.

Copyright
© 2021 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Statistical Theory and Applications
Volume-Issue
20 - 2
Pages
242 - 250
Publication Date
2021/03/26
ISSN (Online)
2214-1766
ISSN (Print)
1538-7887
DOI
https://doi.org/10.2991/jsta.d.210322.001How to use a DOI?
Copyright
© 2021 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Akbar Irandoukht
PY  - 2021
DA  - 2021/03/26
TI  - Optimum Ridge Regression Parameter Using R-Squared of Prediction as a Criterion for Regression Analysis
JO  - Journal of Statistical Theory and Applications
SP  - 242
EP  - 250
VL  - 20
IS  - 2
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.d.210322.001
DO  - https://doi.org/10.2991/jsta.d.210322.001
ID  - Irandoukht2021
ER  -