# CHAPTER 12

# INTRODUCTION TO NONLINEAR REGRESSION

Linear regression models provide a rich and flexible framework that suits the needs of many analysts. However, linear regression models are not appropriate for all situations. There are many problems in engineering and the sciences where the response variable and the predictor variables are related through a known **nonlinear** function. This leads to a **nonlinear regression model**. When the method of least squares is applied to such models, the resulting normal equations are nonlinear and, in general, difficult to solve. The usual approach is to directly minimize the residual sum of squares by an iterative procedure. In this chapter we describe estimating the parameters in a nonlinear regression model and show how to make appropriate inferences on the model parameters. We also illustrate computer software for noulinear regression.

## 12.1 LINEAR AND NONLINEAR REGRESSION MODELS

### 12.1.1 Linear Regression Models

In previous chapters we have concentrated on the **linear regression model**

These models include not only the first-order relationships, such as Eq. (12.1), but also polynomial models and other more complex relationships. In fact, we could write the linear regression model as

where *z*_{i} represents any **function** of the original regressors *x*_{1}