Nonlinear regression is a type of regression analysis in which data follows a model and is then represented as a function of mathematics. Simple linear regression relates to two variables (X and Y) with a straight line function, , whereas nonlinear regression has to generate a curve. Nonlinear regression uses a regression equation, which is as follows:

Let's look at this formula:

• X = A vector of p predictors
• β = A vector of k parameters
• f(-) = A known regression function
• ε = An error term

Nonlinear regression can fit an enormous variety of curves. It uses logarithmic functions, trigonometric functions, exponential functions, and many other fitting methods. This modeling is similar to linear regression modeling because both attempt to graphically control a specific answer from a set of variables. These are more complicated to develop than linear models because the function is generated by means of a series of approximations (iterations) that may result from trial and error. Mathematicians use a variety of established methods, such as the Gauss-Newton and Levenberg-Marquardt methods. The goal of this nonlinear model generated curve line is to make the OLS as small as possible. The smaller the OLS the better the function fits in the dataset's points. It measures how many observations vary from the dataset average.

In the next section, we are going to learn how we can develop and evaluate the regression model using the Python libraries.