Statistics Toolbox

Confidence Intervals on the Predicted Responses

Using nlpredci, form 95% confidence intervals on the predicted responses from the reaction kinetics example.

[yhat,delta] = nlpredci('hougen',reactants,betahat,resid,J);
opd = [rate yhat delta]
opd =
    8.5500    8.2937    0.9178
    3.7900    3.8584    0.7244
    4.8200    4.7950    0.8267
    0.0200   -0.0725    0.4775
    2.7500    2.5687    0.4987
   14.3900   14.2227    0.9666
    2.5400    2.4393    0.9247
    4.3500    3.9360    0.7327
   13.0000   12.9440    0.7210
    8.5000    8.2670    0.9459
    0.0500   -0.1437    0.9537
   11.3200   11.3484    0.9228
    3.1300    3.3145    0.8418

Matrix opd has the observed rates in column 1 and the predictions in column 2. The 95% confidence interval is column 2±column 3. These are simultaneous confidence intervals for the estimated function at each input value. They are not intervals for new response observations at those inputs, even though most of the confidence intervals do contain the original observations.

Confidence Intervals on the Parameter Estimates

An Interactive GUI for Nonlinear Fitting and Prediction