Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-01-08T16:17:26.312Z Has data issue: false hasContentIssue false

Geometrical Representation of Two Methods of Linear Least Squares Multiple Correlation

Published online by Cambridge University Press:  01 January 2025

Benjamin Fruchter
Affiliation:
The University of Texas
Harry E. Anderson Jr.
Affiliation:
American Institute for Research

Abstract

Geometrical properties and relationships of the Doolittle and square root methods of multiple correlation, as represented in the variable subspace of an orthogonal person space, are shown. The method of representation is also useful for depicting zero-order and partial correlations, as well as for the more general problem of the combination of variables.

Type
Original Paper
Copyright
Copyright © 1961 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, H. E. and Fruchter, B. Some multiple correlation and predictor selection methods. Psychometrika, 1960, 25, 5976.CrossRefGoogle Scholar
Bruner, N. Note on the Doolittle solution. Econometrica, 1947, 15, 4344.CrossRefGoogle Scholar
Doolittle, M. H. Method employed in the solution of normal equations and the adjustment of a triangulation. Paper No. 3 in Adjustment of the primary triangulation between Kent Island and Atlantic base lines. Rep. of the Superintendent, Coast and Geodetic Survey, 1878. Pp. 115120.Google Scholar
Durand, D. A note on matrix inversion by the square root method. J. Amer. statist. Ass., 1956, 51, 288292.CrossRefGoogle Scholar
Durbin, J. and Kendall, M. G. The geometry of estimation. Biometrika, 1951, 38, 150158.CrossRefGoogle ScholarPubMed
Dwyer, P. S. The Doolittle technique. Ann. math. Statist., 1941, 12, 449458.CrossRefGoogle Scholar
Dwyer, P. S. The square root method and its use in correlation and regression. J. Amer. statist. Ass., 1945, 40, 493503.CrossRefGoogle Scholar
Dwyer, P. S. Linear computations, New York: Wiley, 1951.Google Scholar
Fruchter, B. Introduction to factor analysis, New York: Van Nostrand, 1954.Google Scholar
Horst, P. A technique for the development of a differential prediction battery. Psychol. Monogr., 1954, 68, No. 9 (Whole No. 380).CrossRefGoogle Scholar
Horst, P. A technique for the development of a multiple absolute prediction battery. Psychol. Monogr., 1955, 69, No. 5 (Whole No. 390).CrossRefGoogle Scholar
Jackson, D. The elementary geometry of function space. Amer. math. Mon., 1924, 31, 461471.CrossRefGoogle Scholar
Leavens, D. Accuracy in the Doolittle solution. Econometrica, 1947, 15, 4550.CrossRefGoogle Scholar
Linhart, H. A criterion for selecting variables in a regression analysis. Psychometrika, 1960, 25, 4558.CrossRefGoogle Scholar
Lubin, A. Some formulae for use with suppressor variables. Educ. psychol. Measmt, 1957, 17, 286296.CrossRefGoogle Scholar
Lubin, A. and Summerfield, A. A square root method of selecting a minimum set of variables in multiple regression: II. A worked example. Psychometrika, 1951, 16, 425437.CrossRefGoogle Scholar
Schweiker, R. F. Individual space models of certain statistics. Unpublished doctoral dissertation, Harvard Univ., 1954.Google Scholar
Stead, W. H. and Shartle, C. L. Occupational counseling techniques, New York: American Book, 1940.Google Scholar
Summerfield, A. and Lubin, A. A square root method of selecting a minimum set of variables in multiple regression: I. The method. Psychometrika, 1951, 16, 271284.CrossRefGoogle Scholar
Walker, H. M. and Lev, J. Statistical inference, New York: Holt, 1953.CrossRefGoogle Scholar