How Many Variables Should Be Entered in a Regression Equation?

How Many Variables Should Be Entered in a Regression Equation?

The optimal number of regressors is determined to minimize mean squared prediction error and is shown to be a small fraction of the number of data points. As the number of regressors grows large, the S p criterion provides an asymptotically optimal rule for the number of variables to enter.

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Bibliographische Detailangaben
Veröffentlicht in:Journal of the American Statistical Association 1983-03, Vol.78 (381), p.131-136
Hauptverfasser: Breiman, L., Freedman, D.
Format: Artikel
Sprache:eng
Schlagworte:
Best subsets regression
Error rates
Linear regression
Mathematical vectors
Matrices
Prediction error
Probabilities
Random errors
Regression
Statistical theories
Statistical variance
Statistics
Stepwise regression
Theory and Methods
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Beschreibung
Zusammenfassung:The optimal number of regressors is determined to minimize mean squared prediction error and is shown to be a small fraction of the number of data points. As the number of regressors grows large, the S p criterion provides an asymptotically optimal rule for the number of variables to enter.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.1983.10477941