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Use of Regression Residuals in the Calculation of Orthogonal Polynomial Coefficients¹

A method is presented for calculating orthogonal polynomial coefficients when the levels of the independent variable are not equally spaced and(or) replicated. The coefficients may be found by using a standard regression computer program or by means of a hand calculator. The method is based on the orthogonality between the computed residuals and the independent variables in a regression analysis.

Key Words: computation • analysis • statistical methodology

² Associate Professor of Statistics, (now, Professor of Statistics, University of Kentucky, Lexington, Ky. 40506), and Professor of Statistics, Iowa State University.

Received for publication August 14, 1967.