Statistics Toolbox

nlpredci

Confidence intervals on predictions of nonlinear models

Syntax

• ypred = nlpredci(FUN,inputs,beta,r,J)
  [ypred,delta] = nlpredci(FUN,inputs,beta,r,J)
  ypred = nlpredci(FUN,inputs,beta,r,J,alpha,'simopt','predopt')
  

Description

ypred = nlpredci(FUN,inputs,beta,r,J) returns the predicted responses, ypred, given the fitted parameters beta, residuals r, and the Jacobian matrix J. inputs is a matrix of values of the independent variables in the nonlinear function.

[ypred,delta] = nlpredci(FUN,inputs,beta,r,J) also returns the half-width, delta, of confidence intervals for the nonlinear least squares predictions. The confidence interval calculation is valid for systems where the length of r exceeds the length of beta and J is of full column rank. The interval [ypred-delta,ypred+delta] is a 95% non-simultaneous confidence interval for the true value of the function at the specified input values.

ypred = nlpredci(FUN,inputs,beta,r,J,alpha,'simopt','predopt') controls the type of confidence intervals. The confidence level is 100(1-alpha)%. 'simopt' can be 'on' for simultaneous intervals or 'off' (the default) for non-simultaneous intervals. 'predopt' can be 'curve' (the default) for confidence intervals for the function value at the inputs, or 'observation' for confidence intervals for a new response value.

nlpredci uses the outputs of nlinfit for its inputs.

Example

Continuing the example from nlinfit, we can determine the predicted function value at [100 300 80] and the half-width of a confidence interval for it.

• load reaction
  [beta,resids,J] = nlinfit(reactants,rate,@hougen,beta);
  [ypred,delta] = nlpredci(@hougen,[100 300 80],beta,resids,J)
  ypred =
      13
  delta =
         1.4277
  

See Also
nlinfit, nlintool, nlparci

nlparci

normcdf