The case for the curve: Parametric regression with second- and third-order polynomial functions of predictors should...

Polynomial regression is an old and commonly discussed modeling technique, though recommendations for its usage are widely variable. Here, we make the case that polynomial regression with second- and third-order terms should be part of every applied practitioners standard model-building toolbox, and should be taught to new students of the subject as the default technique to model nonlinearity. We argue that polynomial regression is superior to nonparametric alternatives for nonstatisticians due to its ease of interpretation, flexibility, and its nonreliance on sophisticated mathematics, like knots and kernel smoothing. This makes it the ideal default for nonstatisticians interested in building realistic models that can capture global as well as local effects of predictors on a response variable. Low-order polynomial regression can effectively model compact floor and ceiling effects, local linearity, and prevent inferring the presence of spurious interaction effects between distinct predictors when none are present. We also argue that the case against polynomial regression is largely specious, relying on either misconceptions around the method, strawman arguments, or historical artifacts. (PsycInfo Database Record (c) 2025 APA, all rights reserved).