This paper provides an introduction to polynomial regression, which is useful for analyzing curvilinear data. I illustrate the power of the procedure with illustrative biological dose-response data based on science fair research. I show an easy-to-implement approach for overcoming an issue common in polynomial regression, namely multicollinearity. I discuss a common criticism of polynomial regression (overfitting) and provide conceptual tools to convert that criticism to a productive discussion point. This paper is geared to a general audience.