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A Square Root Method of Selecting a Minimum Set of Variables in Multiple Regression: I. The Method

Published online by Cambridge University Press:  01 January 2025

A. Summerfield  and
A. Lubin
A. Summerfield
Affiliation:
University College, London
A. Lubin
Affiliation:
Institute of Psychiatry, Maudsley Hospital
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Abstract

An extension of Dwyer's “square root” method has been made to the problem of selecting a minimum set of variables in a multiple regression problem. The square root method of selection differs from the Wherry-Doolittle method primarily in that (1) the computations required are more compact, (2) an F ratio criterion is used which leads to the selection of fewer variables. The method provides solutions for the problems of test selection, item analysis, analysis of variance with disproportionate frequencies, and other problems requiring the rejection of superfluous variables. In a subsequent article a worked example will be given, and the square root and Wherry-Doolittle methods compared.

Type
Original Paper
Information
Psychometrika , Volume 16 , Issue 3 , September 1951 , pp. 271 - 284
Copyright
Copyright © 1951 The Psychometric Society

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References

Burt, Cyri. The factors of the mind, London: Univ. of London Press, 1940.Google Scholar
Dwyer, P. S. The contribution of an orthogonal multiple factor solution to multiple correlation. Psychometrika, 1939, 4, 163–171.CrossRefGoogle Scholar
Dwyer, P. S. The evaluation of multiple and partial correlation coefficients from the factorial matrix. Psychometrika, 1940, 5, 211–232.CrossRefGoogle Scholar
Dwyer, P. S. The square root method and its use in correlation and regression. J. Amer. stat. Ass., 1945, 40, 493–503.CrossRefGoogle Scholar
Fisher, R. A. The precision of discriminant functions. Ann. Eugen., 1940, 10, 422–429.CrossRefGoogle Scholar
Frazer, R. A. Duncan, W. J. Collar, A. R. Elementary matrices, Cambridge: Cambridge University Press, 1947.Google Scholar
Frisch, R. Statistical confluence analysis by means of complete regression equations, Oslo: Universitets Okonomiske Institut, 1934.Google Scholar
Guttman, L. Multiple rectilinear prediction and the resolution into components. Psychometrika, 1940, 5, 75–99.CrossRefGoogle Scholar
Himmelweit, H. T. Summerfield, A. Student selection: II. Brit. J. Sociol., 1951, 2, 59–75.CrossRefGoogle Scholar
Holzinger, K. J. Preliminary report on Spearman-Holzinger unitary trait study, No. 5, Chicago: Statistical Laboratory, Department of Education, Univ. of Chicago, 1934.Google Scholar
Holzinger, K. J. Harman, H. H. Factor analysis, Chicago: Univ. of Chicago Press, 1941.Google Scholar
Horst, P. Smith, S. The discrimination of two racial samples. Psychometrika, 1950, 15, 271–290.CrossRefGoogle ScholarPubMed
Johnson, P. O. Statistical methods in research, New York: Prentice-Hall, 1949.Google Scholar
Kendall, M. G. The advanced theory of statistics, Vol. II, London: Charles Griffin, 1948.Google Scholar
McMahon, J. Hyperpherical goniometry; and its application to correlation theory for n variables. Biometrika, 1923, 15, 173–208.CrossRefGoogle Scholar
McNemar, Q. Psychological statistics, New York: Wiley, 1949.Google Scholar
Mann, H. B. Analysis and design of experiments, New York: Dover Publications, 1949.Google Scholar
Roff, M. Some properties of the communality in multiple factor theory. Psychometrika, 1935, 1, 1–6.CrossRefGoogle Scholar
Thorndike, R. L. Personnel selection: test and measurement techniques, New York: Wiley, 1949.Google Scholar
Thurstone, L. L. Theory of multiple factors, Ann Arbor, Michigan: Edwards Bros., 1932.Google Scholar
Thurstone, L. L. The vectors of mind, Chicago: University of Chicago Press, 1935.Google Scholar
Thurstone, L. L. Multiple-factor analysis, Chicago: Univ. of Chicago Press, 1947.Google Scholar
Tippett, L. H. C. The methods of statistics 3rd ed.,, London: Williams and Norgate, 1948.Google Scholar
Wherry, R. J. In Stead, W. H. Shartle, C. P.(Eds.), Occupational counseling techniques. Appendix V (pp. 245–252). New York: American Book Company, 1940.Google Scholar