线性和非线性回归

用线性或非线性库模型或自定义模型进行曲线或曲面拟合

回归是一种估计一个响应（输出）变量和一个或多个预测变量（输入）变量之间关系的方法。您可以使用线性和非线性回归来预测、预报和估计观察到的数据点之间的值。Curve Fitting Toolbox™ 函数允许您通过使用线性和非线性模型库或自定义方程对数据进行曲线或曲面拟合来执行回归。

您可以使用曲线拟合器以交互方式对数据进行曲线和曲面拟合。有关详细信息，请参阅曲线拟合。您还可以在命令行中使用 fit 函数对一组数据进行曲线或曲面拟合。有关简单示例，请参阅多项式曲线拟合。

App

曲线拟合器

对数据进行曲线和曲面拟合

函数

全部展开

创建拟合

`excludedata`	Exclude data from fit
`fit`	对数据进行曲线或曲面拟合
`fittype`	曲线和曲面拟合的拟合类型
`fitoptions`	创建或修改拟合选项对象
`prepareCurveData`	为曲线拟合准备数据输入
`prepareSurfaceData`	为曲面拟合准备数据输入

使用拟合

`argnames`	`cfit`、`sfit` 或 `fittype` 对象的输入参量名称
`category`	`cfit`、`sfit` 或 `fittype` 对象的拟合类别
`coeffnames`	`cfit`、`sfit` 或 `fittype` 对象的系数名称
`coeffvalues`	`cfit` 或 `sfit` 对象的系数值
`dependnames`	`cfit`、`sfit` 或 `fittype` 对象的因变量
`feval`	评估 `cfit`、`sfit` 或 `fittype` 对象
`formula`	`cfit`、`sfit` 或 `fittype` 对象的公式
`get`	Get fit options structure property names and values
`indepnames`	`cfit`、`sfit` 或 `fittype` 对象的自变量
`islinear`	Determine if `cfit`, `sfit`, or `fittype` object is linear
`numargs`	`cfit`、`sfit` 或 `fittype` 对象的输入参量的数目
`numcoeffs`	`cfit`、`sfit` 或 `fittype` 对象的系数的数目
`probnames`	`cfit`、`sfit` 或 `fittype` 对象的问题相关参数名称
`set`	Assign values in fit options structure
`setoptions`	设置模型拟合选项
`type`	`cfit`、`sfit` 或 `fittype` 对象的名称

主题

教程

参数化拟合
查找曲线拟合器和 fit 函数的所有库模型类型，设置拟合选项，并优化起点。
Introduction to Least-Squares Fitting
Perform least-squares fitting by using error distributions and linear, weighted, robust, and nonlinear least squares.
Polynomial Models
Fit polynomials in the Curve Fitter app or with the fit function.
指数模型
在曲线拟合器中或使用 fit 函数拟合指数模型。
Fit Logarithmic Models
A logarithmic model has a steep initial period of growth before continuing to grow at a slower rate.
Fit Fourier Models
Fit Fourier series models in the Curve Fitter app or with the fit function.
高斯模型
在曲线拟合器中或使用 fit 函数拟合高斯模型。
幂级数
在曲线拟合器中或使用 fit 函数进行幂级数模型拟合。
Rational Models
Fit rational polynomial models in the Curve Fitter app or with the fit function.
正弦和模型
在曲线拟合器中或使用 fit 函数进行正弦和模型拟合。
Weibull Distributions
Fit Weibull distribution models in the Curve Fitter app or with the fit function.
Fit Sigmoidal Models
Sigmoidal models are S-shaped curves that are commonly used to model dose-response curves and population dynamics.
Custom Models
If the Curve Fitting Toolbox library does not contain a desired parametric equation, you can create your own custom equation.
Custom Linear Fitting
In the Curve Fitter app, you can use the Custom Equation fit to define your own linear or nonlinear equations.

工具工作流

交互式曲线和曲面拟合
使用曲线拟合器选择数据和模型类型以进行曲线和曲面拟合，然后保存您的会话。
数据选择
在曲线拟合器中选择要拟合曲线和曲面的数据，确定大小兼容的数据并对数据问题进行故障排除。
Compare Fits in Curve Fitter App
Find the best fit by comparing visual and numeric results, including fitted coefficients and goodness-of-fit statistics.
Surface Fitting to Franke Data
Create and compare surface fits in Curve Fitter 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.

编程工作流

Curve and Surface Fitting
Workflow for programmatic curve and surface fitting in Curve Fitting Toolbox.
曲线和曲面拟合的库模型列表
查找使用 fit 函数进行编程数据拟合所需的所有 Curve Fitting Toolbox 库模型名称。
Curve and Surface Fitting Objects and Object Functions
Learn how to create, access, and modify curve and surface fit objects.
多项式曲线拟合
此示例说明如何使用 Curve Fitting Toolbox 对部分人口普查数据进行最高六次的多项式拟合。
Fit Polynomial Model to Data
This example shows how to fit a polynomial model to data using the linear least-squares method.
Compare Robust Fitting Methods
This example shows how to fit a polynomial model to data using the bisquare weights, least absolute residuals (LAR), and linear least-squares methods.
自定义非线性人口普查拟合
此示例说明如何对人口普查数据进行自定义方程拟合，指定边界、系数和问题相关参数。
对数据进行指数模型拟合
此示例说明如何使用信赖域和莱文贝格-马夸特非线性最小二乘算法对数据进行指数模型拟合。
Improve Model Fit with Weights
This example shows how to fit a polynomial model to data using both the linear least-squares method and the weighted least-squares method for comparison.
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.

精选示例

多项式曲线拟合

此示例说明如何使用 Curve Fitting Toolbox 对部分人口普查数据进行最高六次的多项式拟合。

打开实时脚本

自定义非线性人口普查拟合

此示例说明如何对人口普查数据进行自定义方程拟合，指定边界、系数和问题相关参数。

打开实时脚本

Surface Fitting with Custom Equations to Biopharmaceutical Data

Use Curve Fitting Toolbox™ to fit response surfaces to some anesthesia data to analyze drug interaction effects. Response surface models provide a good method for understanding the pharmacodynamic interaction behavior of drug combinations.