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Obtaining Squared Multiple Correlations from a Correlation Matrix which may be Singular

Published online by Cambridge University Press:  01 January 2025

Ledyard R Tucker ,
Lee G. Cooper  and
William Meredith
Ledyard R Tucker
Affiliation:
University of Illinois
Lee G. Cooper
Affiliation:
University of California, Los Angeles
William Meredith
Affiliation:
University of California, Berkeley
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Abstract

A theorem is presented relating the squared multiple correlation of each measure in a battery with the other measures to the unique generalized inverse of the correlation matrix. This theorem is independent of the rank of the correlation matrix and may be utilized for singular correlation matrices. A coefficient is presented which indicates whether the squared multiple correlation is unity or not. Note that not all measures necessarily have unit squared multiple correlations with the other measures when the correlation matrix is singular. Some suggestions for computations are given for simultaneous determination of squared multiple correlations for all measures.

Type
Original Paper
Information
Psychometrika , Volume 37 , Issue 2 , June 1972 , pp. 143 - 148
Copyright
Copyright © 1972 The Psychometric Society

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Footnotes

*

The research reported in this paper was supported by the Personnel and Training Branch of the Office of Naval Research under Contract Number 00014-67-A-0305-0003 with the University of Illinois.

References

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