APA Dictionary of Psychology

a type of linear regression analysis in which the relationship between an explanatory or independent variable and an outcome or dependent variable is modeled as a polynomial. Polynomial regression is appropriate for expressing higher order nonlinear effects among variables (via quadratic or cubic functions such as y_i = β₀ + β₁x_i + β₂x_i² + β₃x_i³ + …) while retaining all other aspects of linear approaches.