# Documentation

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# Linear and Nonlinear Regression

Fit curves or surfaces with linear and nonlinear library models and custom models

## Apps

 Curve Fitting Fit curves and surfaces to data

## Functions

 `fit` Fit curve or surface to data `fittype` Fit type for curve and surface fitting `fitoptions` Create or modify fit options object `prepareCurveData` Prepare data inputs for curve fitting `prepareSurfaceData` Prepare data inputs for surface fitting `excludedata` Exclude data from fit
 `argnames` Input argument names of cfit, sfit, or fittype object `category` Category of fit of cfit, sfit, or fittype object `coeffnames` Coefficient names of cfit, sfit, or fittype object `coeffvalues` Coefficient values of cfit or sfit object `dependnames` Dependent variable of cfit, sfit, or fittype object `feval` Evaluate cfit, sfit, or fittype object `formula` Formula of cfit, sfit, or fittype object `get` Get fit options structure property names and values `indepnames` Independent variable of cfit, sfit, or fittype object `islinear` Determine if cfit, sfit, or fittype object is linear `numargs` Number of input arguments of cfit, sfit, or fittype object `numcoeffs` Number of coefficients of cfit, sfit, or fittype object `probnames` Problem-dependent parameter names of cfit, sfit, or fittype object `set` Assign values in fit options structure `setoptions` Set model fit options `type` Name of cfit, sfit, or fittype object

## Examples and How To

### Tutorials

Polynomial Models

Fit polynomials in Curve Fitting app or with the `fit` function.

Exponential Models

Fit exponential models in Curve Fitting app or with the `fit` function.

Fourier Series

Fit Fourier series models in Curve Fitting app or with the `fit` function.

Gaussian Models

Fit Gaussian models in Curve Fitting app or with the `fit` function.

Power Series

Fit power series models in Curve Fitting app or with the `fit` function.

Rational Polynomials

Fit rational polynomial models in Curve Fitting app or with the `fit` function.

Sum of Sines Models

Fit sum of sines models in Curve Fitting app or with the `fit` function.

Weibull Distributions

Fit Weibull distribution models in Curve Fitting app or with the `fit` function.

Custom Models

If the toolbox library does not contain a desired parametric equation, you can create your own custom equation.

### Tools Workflow

Interactive Curve and Surface Fitting

Fit curves and surfaces to data using Curve Fitting app: select data, choose model types, and save sessions.

Data Selection

Select data to fit curves and surfaces in Curve Fitting app, identify compatible size data and troubleshoot data problems.

Compare Fits in Curve Fitting App

Search for the best fit by creating multiple fits, comparing graphical and numerical results including fitted coefficients and goodness-of-fit statistics, and analyzing your best fit in the workspace.

Surface Fitting to Franke Data

Create and compare surface fits in Curve Fitting app using example data.

Surface Fitting to Biopharmaceutical Data

Curve Fitting Toolbox™ software provides some example data for an anesthesia drug interaction study.

Custom Nonlinear ENSO Data Analysis

This example fits the ENSO data using several custom nonlinear equations.

Gaussian Fitting with an Exponential Background

This example fits two poorly resolved Gaussian peaks on a decaying exponential background using a general (nonlinear) custom model.

### Programmatic Workflow

Curve and Surface Fitting

Workflow for programmatic curve and surface fitting in Curve Fitting Toolbox.

Polynomial Curve Fitting

This example shows how to fit polynomials up to sixth degree to some census data using Curve Fitting Toolbox™.

Custom Nonlinear Census Fitting

This example shows how to fit a custom equation to census data, specifying bounds, coefficients, and a problem-dependent parameter.

Surface Fitting With Custom Equations to Biopharmaceutical Data

This example shows how to use Curve Fitting Toolbox™ to fit response surfaces to some anesthesia data to analyze drug interaction effects.

## Concepts

Parametric Fitting

Find all library model types for Curve Fitting app and the `fit` function, set fit options and optimize starting points.

Least-Squares Fitting

Least-squares fitting in Curve Fitting Toolbox, including error distributions, linear, weighted, robust, and nonlinear least squares.