nlinfit (Statistics Toolbox)

Nonlinear least-squares data fitting by the Gauss-Newton method

Syntax

beta = nlinfit(X,y,FUN,beta0)
[beta,r,J] = nlinfit(X,y,FUN,beta0)

Description

beta = nlinfit(X,y,FUN,beta0) estimates the coefficients of a nonlinear function using least squares. y is a vector of response (dependent variable) values. Typically, X is a design matrix of predictor (independent variable) values, with one row for each value in y. However, X can be any array that FUN can accept. FUN is a function of the form

```
yhat = myfun(beta,X)
```

where beta is a coefficient vector, and X is the design matrix. FUN returns a vector yhat of fitted y values. beta0 is a vector containing initial values for the coefficients.

[beta,r,J] = nlinfit(X,y,FUN,beta0) returns the fitted coefficients, beta, the residuals, r, and the Jacobian, J. You can use these outputs with nlpredci to produce error estimates on predictions, and with nlparci to produce error estimates on the estimated coefficients.

Note nlintool provides a GUI for performing nonlinear fits and computing confidence intervals.

Example

Find the coefficients that best fit the data in reaction.mat. The chemistry behind this data set deals with reaction kinetics as a function of the partial pressure of three chemical reactants: hydrogen, n-pentane, and isopentane.

The hougen function uses the Hougen-Watson model for reaction kinetics to return the predicted values of the reaction rate.

load reaction
betafit = nlinfit(reactants,rate,@hougen,beta)
betafit =
    1.2526
    0.0628
    0.0400
    0.1124
    1.1914

See Also
hougen, nlintool, nlparci, nlpredci

ncx2stat nlintool