Nonlinear least squares
In Chapter 3, More Than Just One Predictor – MLR, we have already handled a case in which a linear regression was unable to model the relationship between the response and predictors. In that case, we solved the problem by applying polynomial regression. When the relationships between variables are not linear, three solutions are possible:
- Linearize the relationship by transforming the data
- Fit polynomial or complex spline models
- Fit a nonlinear model
The first two solutions you have already faced in somemanner in the previous chapters. Now we will focus on the third solution. If the parameters of the regression function to be estimated are nonlinear, that is, they appear at a different degree from the first, the Ordinary Least Squares (OLS) can no longer be applied and other methods need to be applied.
In the multiple nonlinear regression models, the dependent variable is related to two or more independent variables as follows:
Here, the model is not linear with respect...
