In social-behavioral sciences, the term polynomial concerns the use of exponents or special coefficients to assess trends in linear models, with applications in ordinary least squares (OLS) regression, general linear model (GLM) analysis of variance (ANOVA), and other advanced multivariate applications such as hierarchical linear modeling, logistic regression, and generalized estimating equations. In more formal mathematics, polynomials are algebraic expressions that include exponents and have other specific properties. The simplest case of a polynomial is the OLS linear regression equation Y = A + bX1 (in OLS regression, X1 is typically represented as X). One of the earliest examples of polynomials to assess trends can be traced to Karl Pearson's 1905 work addressing “skew correlation,” where he used an exponent approach to assess nonlinear ...

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