Obtaining Squared Multiple Correlations from a Correlation Matrix which may be Singular
- 1 June 1972
- journal article
- Published by Cambridge University Press (CUP) in Psychometrika
- Vol. 37 (2) , 143-148
- https://doi.org/10.1007/bf02306772
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.Keywords
This publication has 3 references indexed in Scilit:
- A generalized inverse for matricesMathematical Proceedings of the Cambridge Philosophical Society, 1955
- Multiple Rectilinear Prediction and the Resolution into ComponentsPsychometrika, 1940
- Some Properties of the Communality in Multiple Factor TheoryPsychometrika, 1936