Statistics Toolbox

Example: Nonlinear Modeling

The Hougen-Watson model (Bates and Watts 1988) for reaction kinetics is one specific example of this type. The form of the model is

where ₁, ₂, ...,₅ are the unknown parameters, and x₁, x₂, and x₃ are the three input variables. The three inputs are hydrogen, n-pentane, and isopentane. It is easy to see that the parameters do not enter the model linearly.

The file reaction.mat contains simulated data from this reaction.

load reaction
who
Your variables are:
beta        rate        xn          
model       reactants   yn          

The variables are as follows:

• rate is a 13-by-1 vector of observed reaction rates.
• reactants is a 13-by-3 matrix of reactants.
• beta is 5-by-1 vector of initial parameter estimates.
• model is a string containing the nonlinear function name.
• xn is a string matrix of the names of the reactants.
• yn is a string containing the name of the response.

The data and model are explored further in the following sections:

• Fitting the Hougen-Watson Model
• Confidence Intervals on the Parameter Estimates
• Confidence Intervals on the Predicted Responses
• An Interactive GUI for Nonlinear Fitting and Prediction

Nonlinear Regression Models

Fitting the Hougen-Watson Model