Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-01-08T11:52:03.249Z Has data issue: false hasContentIssue false

A Note on the Estimation of the Level of Predictive Precision of a Fitted Linear Equation

Published online by Cambridge University Press:  01 January 2025

Jorge L. Mendoza*
Affiliation:
University of Georgia
*
Requests for reprints should be sent to Jorge L. Mendoza, Psychology Department, University of Georgia, Athens, Georgia 30602.

Abstract

A procedure that utilizes the sample multiple correlation to form a lower bound for the level of predictive precision of a fitted regression equation is suggested. The procedure is shown to yield probability statements which are true at least 100(1−α)% of the time.

Type
Notes And Comments
Copyright
Copyright © 1977 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

Reference Notes

Claudy, J. G. An empirical investigation of small sample multiple regression and cross-validation. Unpublished doctoral dissertation, University of Tennessee, 1969.Google Scholar
Lord, F. M. Efficiency of prediction when a regression equation from one sample is used in a new sample, 1950, Princeton, New Jersey: Educational Testing Service.CrossRefGoogle Scholar

References

Burkett, G. R. A study of reduced rank models for multiple prediction. Psychometric Monographs, 1964, No. 12.Google Scholar
Darlington, R. B. Multiple regression in psychological research and practice. Psychological Bulletin, 1969, 69, 161182.CrossRefGoogle Scholar
Ezekiel, M. A. & Fox, K. A. Methods of correlation and regression, 1959, New York: Wiley.Google Scholar
Fisher, R. A. The general sampling distribution of the multiple correlation coefficient. Proceedings of the Royal Society of London, 1928, 121, 654673.Google Scholar
Graybill, F. A. An introduction to linear statistical models, 1961, New York: McGraw-Hill.Google Scholar
Gross, A. L. Prediction in future samples studied in terms of the gain from selection. Psychometrika, 1973, 38, 151172.CrossRefGoogle Scholar
Hertzberg, P. A. The parameters of cross-validation, Psychometrika Monograph Supplement, 1969, 34, (16).Google Scholar
Kramer, K. H. Tables for constructing confidence limits on the multiple correlation coefficient. Journal of the American Statistical Association, 1963, 58, 10821085.CrossRefGoogle Scholar
Park, C. N. & Dudycha, A. L. A cross-validation approach to sample size determination for regression models. Journal of the American Statistical Association, 1974, 69, 214215.CrossRefGoogle Scholar
Resnikoff, G. J. & Lieberman, G. J. Tables of the Noncentral t Distribution, 1957, Stanford: Stanford University Press.Google Scholar