The Curve Fitting app simplifies common tasks that include:

• Importing data from the MATLAB^® workspace
• Visualizing your data to perform exploratory data analysis
• Generating fits using multiple fitting algorithms
• Evaluating the accuracy of your models
• Performing postprocessing analysis that includes interpolation and extrapolation, generating confidence intervals, and calculating integrals and derivatives
• Exporting fits to the MATLAB workspace for further analysis
• Automatically generating MATLAB code to capture work and automate tasks

Working at the command line lets you develop custom functions for analysis and visualization. These functions enable you to:

• Duplicate your analysis with a new data set
• Replicate your analysis with multiple data sets (batch processing)
• Embed a fitting routine into MATLAB functions
• Extend the base capabilities of the toolbox

Curve Fitting Toolbox provides a simple intuitive syntax for command-line fitting, as in the following examples:

• Linear Regression: fittedmodel = fit([X,Y], Z, 'poly11');
• Nonlinear Regression: fittedmodel = fit(X, Y, 'fourier2');
• Interpolation: fittedmodel = fit([Time,Temperature], Energy, 'cubicinterp');
• Smoothing: fittedmodel = fit([Time,Temperature], Energy, 'lowess', ‘span’, 0.12);

The results of a fitting operation are stored in an object called “fittedmodel.” Postprocessing analysis, such as plotting, evaluation, and calculating integrals and derivatives, can be performed by applying a method to this object, as in these examples:

• Plotting: plot(fittedmodel)
• Differentiation: differentiate(fittedmodel, X, Y)
• Evaluation: fittedmodel(80, 40)

Curve Fitting Toolbox lets you move interactive fitting to the command line. Using the app, you can automatically generate MATLAB code. You can also create fit objects with the app and export them to the MATLAB workspace for further analysis.

The toolbox supports over 100 regression models, including:

• Lines and planes
• High order polynomials (up to ninth degree for curves and fifth degree for surfaces)
• Fourier and power series
• Gaussians
• Weibull functions
• Exponentials
• Rational functions
• Sum of sines

All of these standard regression models include optimized solver parameters and starting conditions to improve fit quality. Alternatively, you can use the Custom Equation option to specify your own regression model.

In the Curve Fitting app you can generate fits based on complicated parametric models by using a drop-down menu. At the command line you can access the same models using intuitive names.

The regression analysis options in Curve Fitting Toolbox enable you to:

• Choose between two types of robust regression: bisquare or least absolute residual
• Specify starting conditions for the solvers
• Constrain regression coefficients
• Choose Trust-Region or Levenberg-Marquardt algorithms

Explore gallery (3 images)

Curve Fitting Toolbox provides a wide range of descriptive statistics, including:

• R-square and adjusted R-square
• Sum of squares due to errors and root mean squared error
• Degrees of freedom

The Table of Fits lists all of the candidate models in a sortable table, enabling you to quickly compare and contrast multiple models.

The toolbox enables you to visually inspect candidate models to reveal problems with fit that are not apparent in summary statistics. For example, you can:

• Generate side-by-side surface and residual plots to search for patterns in the residuals
• Simultaneously plot multiple models to compare how well they fit the data in critical regions
• Plot the differences between two models as a new surface

Curve Fitting Toolbox supports validation techniques that help protect against overfitting. You can generate a predictive model using a training data set, apply your model to a validation data set, and then evaluate goodness of fit.