Statistics Toolbox

Nonlinear Least Squares

Response Surface Methodology (RSM) is an empirical modeling approach using polynomials as local approximations to the true input/output relationship. This empirical approach is often adequate for process improvement in an industrial setting.

In scientific applications there is usually relevant theory that allows us to make a mechanistic model. Often such models are nonlinear in the unknown parameters. Nonlinear models are more difficult to fit, requiring iterative methods that start with an initial guess of the unknown parameters. Each iteration alters the current guess until the algorithm converges.

The Statistics Toolbox has functions for fitting nonlinear models of the form

where:

• y is an-n by-1 vector of observations.
• f is any function of X and .
• X is an n-by-p matrix of input variables.
• is a p-by-1 vector of unknown parameters to be estimated.
• is an n-by-1 vector of random disturbances.

This is explored further in the following sections:

• Example: Nonlinear Modeling
• An Interactive GUI for Nonlinear Fitting and Prediction

Nonlinear Regression Models

Example: Nonlinear Modeling