# Curve Fitting Toolbox

## Fit curves and surfaces to data using regression, interpolation, and smoothing

Curve Fitting Toolbox™ provides an app and functions for fitting curves and surfaces to data. The toolbox lets you perform exploratory data analysis, preprocess and post-process data, compare candidate models, and remove outliers. You can conduct regression analysis using the library of linear and nonlinear models provided or specify your own custom equations. The library provides optimized solver parameters and starting conditions to improve the quality of your fits. The toolbox also supports nonparametric modeling techniques, such as splines, interpolation, and smoothing.

After creating a fit, you can apply a variety of post-processing methods for plotting, interpolation, and extrapolation; estimating confidence intervals; and calculating integrals and derivatives.

## Curve Fitting App

Import data from the MATLAB workspace and fit curves and surfaces. Conduct linear and nonlinear regression and interpolation.

### Curve Fitting App

Fit curves using the Curve Fitting app or command-line fit functions.

### Surface Fitting

Fit surfaces using the Curve Fitting app or command-line fit functions.

## Linear and Nonlinear Regression

Model a continuous response variable as a function of predictors using linear and nonlinear regression.

### Linear Fitting

Apply linear regression by choosing from standard regression models or by using custom equations. All of the standard regression models include optimized solver parameters and starting conditions to improve fit quality.

### Nonlinear Fitting

Apply nonlinear parametric regression using exponentials, Fourier series, power series, Gaussians, and standard models.

## Smoothing and Interpolation

Use interpolation to estimate values between known data points, and fit using smoothing splines and localized regression to smooth data.

### Interpolation

Fit interpolating curves or surfaces, and estimate values between known data points.

### Smoothing

Smooth data with moving average, smoothing splines, and localized regression.

## Postprocessing

After fitting a curve or surface, use postprocessing methods to plot the fit. Analyze if it is accurate, estimate confidence intervals, and calculate integrals and derivates.

### Compare and Evaluate Fits

Create multiple fits, compare graphical and numerical results, and goodness-of-fit statistics. Use validation data to refine your fit.

### Plotting

Customize plotting and perform additional analyses such as outliers, residuals, confidence intervals, integrals, and derivatives.

## Splines

Construct splines with or without data. Control advanced spline operations including break/knot manipulation, optimal knot placement, and data-point weighting.

### Fitting Splines to Data

Fit various splines to data, including cubic and smoothing splines with various end conditions, for curves, surfaces, and higher dimensional objects.

### B-Splines, Rational Splines, and NURBS

Create B-Splines and Uniform and Non-uniform Rational Splines (NURBS) for analysis of complex surfaces.