, Volume 46, Issue 2, pp 161–169 | Cite as

An optimal property of least squares weights in prediction models

  • Alan L. Gross


In predicting\(\tilde y\) scores fromp > 1 observed scores\((\tilde x)\) in a sample of sizeñ, the optimal strategy (minimum expected loss), under certain assumptions, is shown to be based upon the least squares regression weights\((\hat \beta )\) computed from a previous sample. Letting\(\tilde r(\hat \beta )\) represent the correlation between\(\tilde y\) and the predicted values\((\hat \beta '\tilde x)\), and letting\(\tilde r(w)\) represent the correlation between\(\tilde y\) and a different set of predicted values\((w'\tilde x)\), where w is any weighting system which is not a function of\(\tilde y\), it is shown that the probability of\(\tilde r(\hat \beta )\) being less than\(\tilde r(w)\) cannot exceed .50. The relationship of this result to previous research and practical implications are discussed.

Key words

least squares weights prediction cross validity noninformative prior distribution 


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Reference note

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Copyright information

© The Psychometric Society 1981

Authors and Affiliations

  • Alan L. Gross
    • 1
  1. 1.Graduate Center, City University of New York, Ph.D. Program in Educational PsychologyNew York

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