Hostname: page-component-745bb68f8f-hvd4g Total loading time: 0 Render date: 2025-01-07T19:11:07.587Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Multiple Correlation and Predictor Selection Methods

Published online by Cambridge University Press:  01 January 2025

Harry E. Anderson Jr.  and
Benjamin Fruchter
Harry E. Anderson Jr.
Affiliation:
System Development Corporation
Benjamin Fruchter
Affiliation:
The University of Texas
Get access Rights & Permissions [Opens in a new window]

Abstract

The Doolittle, Wherry-Doolittle, and Summerfield-Lubin methods of multiple correlation are compared theoretically as well as by an application in which a set of predictors is selected. Wherry's method and the Summerfield-Lubin method are shown to be equivalent; the relationship of these methods to the Doolittle method is indicated. The Summerfield-Lubin method, because of its compactness and ease of computation, and because of the meaningfulness of the interim computational values, is recommended as a convenient least squares method of multiple correlation and predictor selection.

Type
Original Paper
Information
Psychometrika , Volume 25 , Issue 1 , March 1960 , pp. 59 - 76
Copyright
Copyright © 1960 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. and Fruchter, B. Procedural studies: the computation of an inverse matrix, Austin: Psychometric Lab., Dept. Educ. Psychol., Univ. Texas, 1957.Google Scholar
Cowles, J. T. A labor-saving method of computing multiple correlation coefficients, regression weights, and standard errors of regression weights. Lackland Air Force Base: Air Training Command, Psychological Research and Examining Unit, 1948. (Mimeo.).Google 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. 115–120.Google Scholar
DuBois, P. H. Multivariate correlational analysis, New York: Harper, 1957.Google Scholar
Durand, D. A note on matrix inversion by the square root method. J. Amer. statist. Ass., 1956, 51, 288–292.CrossRefGoogle Scholar
Dwyer, P. S. The Doolittle technique. Ann. math. Statist., 1941, 12, 449–458.CrossRefGoogle Scholar
Dwyer, P. S. The square root method and its use in correlation and regression. J. Amer. statist. Ass., 1945, 40, 493–503.CrossRefGoogle Scholar
Dwyer, P. S. Pearsonian correlation coefficients associated with least squares theory. Ann. math. Statist., 1949, 20, 404–417.CrossRefGoogle Scholar
Fleishman, E. A., Roberts, M. M., and Friedman, M. P. A factor analysis of aptitude and proficiency measures in radiotelegraphy. J. appl. Psychol., 1958, 42, 129–135.CrossRefGoogle Scholar
Fruchter, B. Note on the computation of the inverse of a triangular matrix. Psychometrika, 1949, 14, 89–93.CrossRefGoogle ScholarPubMed
Fruchter, B. Introduction to factor analysis, New York: Van Nostrand, 1954.Google Scholar
Guilford, J. P. (Ed.) Printed classification tests. AAF Aviation Psychol. Prog. Res. Rep. No. 5, 1945.Google Scholar
Guilford, J. P. Fundamental statistics in psychology and education, New York: McGraw-Hill, 1956.Google Scholar
Guttman, L. Comment on Tryon's formulation of the communality problem, Berkeley: Univ. Calif., 1957.Google Scholar
Horst, P. A short method for solving for a coefficient of multiple correlation. Ann. math. Statist., 1932, 3, 40–45.CrossRefGoogle 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
Kendall, M. G. A course in multivariate analysis, New York: Hafner, 1957.Google 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, 425–437.CrossRefGoogle Scholar
Roff, M. Some properties of the communality in multiple factor theory. Psychometrika, 1936, 1, 1–6.CrossRefGoogle Scholar
Stead, W. H. and Shartle, C. L. Occupational counseling techniques, New York: American Book Co., 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, 271–284.CrossRefGoogle Scholar
Thorndike, R. L. Personnel selection: test and measurement techniques, New York: Wiley, 1949.Google Scholar
Walker, H. M. and Lev, J. Statistical inference, New York: Holt, 1953.CrossRefGoogle Scholar
Wherry, R. J. A new formula for predicting the shrinkage of the coefficient of multiple correlation. Ann. math. Statist., 1931, 2, 440–451.CrossRefGoogle Scholar