Statistics Toolbox™

nlparci - Nonlinear regression parameter confidence intervals

Syntax

ci = nlparci(beta,resid,'covar',sigma)
ci = nlparci(beta,resid,'jacobian',J)
ci = nlparci(...,'alpha',alpha)

Description

ci = nlparci(beta,resid,'covar',sigma) returns the 95% confidence intervals ci for the nonlinear least squares parameter estimates beta. Before calling nlparci, use nlinfit to fit a nonlinear regression model and get the coefficient estimates beta, residuals resid, and estimated coefficient covariance matrix sigma.

ci = nlparci(beta,resid,'jacobian',J) is an alternative syntax that also computes 95% confidence intervals. J is the Jacobian computed by nlinfit. If the 'robust' option is used with nlinfit, use the 'covar' input rather than the 'jacobian' input so that the required sigma parameter takes the robust fitting into account.

ci = nlparci(...,'alpha',alpha) returns 100(1-alpha)% confidence intervals.

nlparci treats NaNs in resid or J as missing values, and ignores the corresponding observations.

The confidence interval calculation is valid for systems where the length of resid exceeds the length of beta and J has full column rank. When J is ill-conditioned, confidence intervals may be inaccurate.

Example

Continuing the example from nlinfit:

load reaction

[beta,resid,J,Sigma] = ...
     nlinfit(reactants,rate,@hougen,beta);

ci = nlparci(beta,resid,'jacobian',J)
ci =
   -0.7467    3.2519
   -0.0377    0.1632
   -0.0312    0.1113
   -0.0609    0.2857
   -0.7381    3.1208

See Also

nlinfit, nlpredci

nlintool

nlpredci