Nonlinear Regression Fitting Tool

R2026b

Interactive nonlinear regression fitting

Description

The Nonlinear Regression Fitting tool allows you to perform simple interactive nonlinear fitting with the nlinfit function.

For more complex workflows, you can use plotSlice with the fitnlm function (see Nonlinear Regression Workflow). The interface displays plots of the fitted response against each predictor, with the other predictors held fixed. Dashed red curves show 95% simultaneous confidence bounds for the function. The fixed values are displayed in the text boxes below each predictor axis. Change the fixed values by entering new values or by dragging the vertical lines in the plots to new positions. When you change the value of a predictor, the tool updates all plots to display the model at the new point in the predictor space. Use the Export button to export specified variables to the workspace.

Required Products

• MATLAB^®

• Statistics and Machine Learning Toolbox™

Open the Nonlinear Regression Fitting Tool

• At the MATLAB command prompt, enter nlintool.

Examples

Nonlinear Regression Fitting with Interactive Tool

Perform nonlinear regression and display fitted model responses for different predictor values using the Nonlinear Regression Fitting tool.

Load the reaction kinetics data set. The observations in reactants are partial pressures of the three chemical reactants listed in xn. The corresponding reaction rates (responses) are stored in rate.

load reaction

Fit the Hougen-Watson model to the data using the initial model coefficient values in beta. Specify to show 99% confidence bounds and to label the plot axes.

nlintool(reactants,rate,@hougen,beta,Alpha=0.01,XName=xn,YName=yn)

The tool displays plots of the fitted response against each predictor. The solid green curve shows the predicted response for that predictor when the other predictor values are fixed. You can change the fixed values by entering new values in the text boxes, or by dragging the vertical lines in the plots to new positions. When you change the value of a predictor, the tool updates all plots to display the model at the new point in the predictor space. The dashed red lines indicate the 99% confidence bounds.

Related Examples

• Nonlinear Regression Workflow

Parameters

Predictors — Fixed predictor values

numeric values

Specify the fixed predictor values as numeric values. Change a fixed predictor value by entering a new value in the field below a plot, or by dragging a vertical line in a plot to a new position.

Bounds — Confidence bounds

Simultaneous | Non-Simultaneous | Curve | Observation

Use the Bounds menu in the tool window to select the type of confidence bounds: simultaneous or non-simultaneous, and curve or observation.

• Simultaneous or Non-Simultaneous

  • Simultaneous (default) — Use Scheffé's method to compute the confidence bounds for the curve of the response values. The range between the upper and lower confidence bounds contains the curve consisting of true response values with 95% confidence.

  • Non-Simultaneous — Compute confidence bounds for the response value at each observation. The confidence interval for a response value at a specific predictor value contains the true response value with 95% confidence.

  With simultaneous bounds, the entire curve of true response values is within the bounds at high confidence. By contrast, non-simultaneous bounds require only the response value at a single predictor value to be within the bounds at high confidence. Therefore, simultaneous bounds are wider than non-simultaneous bounds.

• Curve or Observation

  A regression model for the predictor variables X and the response variable Y has the form

  Y = f(X) + ε,

  where f is a function of X and ε is a random noise term.

  • Curve (default) — Plot confidence bounds for the fitted responses f(X).

  • Observation — Plot confidence bounds for the response observations Y.

  The bounds for Y are wider than the bounds for f(X) because of the noise term.

• If you do not want to display confidence bounds, select No Bounds.

Programmatic Use

nlintool opens the Nonlinear Regression Fitting tool with a nonlinear Hougen-Watson model (hougen) fit to sample reaction rate data (see Nonlinear Regression Fitting with Interactive Tool).

nlintool(X,Y,modelfun,beta0) opens the Nonlinear Regression Fitting tool and displays the fitted response Y against each predictor in X, with the other predictors held fixed. The software generates the fitted responses using the model specified by modelfun and the initial coefficient values beta0. You must specify modelfun as a function handle (see modelfun). Dashed red curves show 95% simultaneous confidence bounds for the function.

nlintool(___,Name=Value) specifies additional options using one or more of the following name-value arguments.

• Alpha — Significance level for the confidence bounds, specified as a nonnegative scalar. Dashed red curves show 100(1 – Alpha)% simultaneous confidence bounds for the function. The default value of Alpha is 0.05.

• XName — Predictor names, specified as a string array, cell array of strings, or character array.

• YName — Response name, specified as a string scalar, cell array containing one character vector, or character vector.

• PlotData — Flag to display the data on the plot, specified as "on" or "off". If X contains more than one predictor, then you cannot specify PlotData="on".

Tips

• Click the Export button to export the fitted parameters and confidence intervals, the root mean squared error (RSME) of the fit, and the fit residuals to the workspace. Adjust the variable names and clear any check boxes in the Export to Workspace dialog box, if necessary, and click OK.

Version History

Introduced before R2006a