Nonlinear regression is a form of regression analysis in which data is fit to a model and then expressed as a mathematical function. Simple linear regression relates two variables (X and Y) with a straight line (y = mx + b), while nonlinear regression relates the two variables in a nonlinear (curved) relationship.

The goal of the model is to make the sum of the squares as small as possible.  The sum of squares is a measure that tracks how far the Y observations vary from the nonlinear (curved) function that is used to predict Y.