Tolerance and Condition in Regression Computations
- 1 December 1977
- journal article
- theory and-method
- Published by Taylor & Francis in Journal of the American Statistical Association
- Vol. 72 (360a) , 863-866
- https://doi.org/10.1080/01621459.1977.10479972
Abstract
Many regression programs include a tolerance test that does not allow a variable to enter the regression if its correlation with the previously entered variables exceeds a specified level. This is done to achieve computational stability by assuring that the correlation matrix C of the independent variables is not nearly singular. However, for any specified tolerance level, there is an example in which the entering variables pass the tolerance test but the computation is extremely unstable. A bound for the condition of C is p times the trace of C -1, which can be monitored instead of tolerance to assure stability.Keywords
This publication has 7 references indexed in Scilit:
- The Acceptability of Regression Solutions: Another Look at Computational AccuracyJournal of the American Statistical Association, 1976
- The Effect of Errors in the Independent Variables in Linear RegressionBiometrika, 1975
- Ridge Regression in PracticeThe American Statistician, 1975
- Regressions by Leaps and BoundsTechnometrics, 1974
- Algorithm AS 79: Gram-Schmidt RegressionJournal of the Royal Statistical Society Series C: Applied Statistics, 1974
- Algorithm AS 60: Latent Roots and Vectors of a Symmetric MatrixJournal of the Royal Statistical Society Series C: Applied Statistics, 1973
- Generalized Inverses, Ridge Regression, Biased Linear Estimation, and Nonlinear EstimationTechnometrics, 1970