多元线性回归

具有多个预测变量的线性回归

为了提高在中低维数据集上的准确度，可以使用 fitlm 拟合线性回归模型。

为了减少在高维数据集上的计算时间，可以使用 fitrlinear 拟合线性回归模型。

App

Train regression models to predict data using supervised machine learning

对象

`LinearModel`	Linear regression model
`CompactLinearModel`	Compact linear regression model
`RegressionLinear`	Linear regression model for high-dimensional data
`RegressionPartitionedLinear`	Cross-validated linear regression model for high-dimensional data

函数

全部展开

`LinearModel` 和 `CompactLinearModel` 函数

创建 `LinearModel` 对象

`fitlm`	拟合线性回归模型
`stepwiselm`	Perform stepwise regression

创建 `CompactLinearModel` 对象

compact Compact linear regression model

添加或删除线性模型中的项

`addTerms`	Add terms to linear regression model
`removeTerms`	Remove terms from linear regression model
`step`	Improve linear regression model by adding or removing terms

预测响应

`feval`	Predict responses of linear regression model using one input for each predictor
`predict`	Predict responses of linear regression model
`random`	Simulate responses with random noise for linear regression model

计算线性模型

`anova`	Analysis of variance for linear regression model
`coefCI`	Confidence intervals of coefficient estimates of linear regression model
`coefTest`	Linear hypothesis test on linear regression model coefficients
`dwtest`	Durbin-Watson test with linear regression model object
`partialDependence`	Compute partial dependence

可视化线性模型和汇总统计量

`plot`	Scatter plot or added variable plot of linear regression model
`plotAdded`	Added variable plot of linear regression model
`plotAdjustedResponse`	Adjusted response plot of linear regression model
`plotDiagnostics`	Plot observation diagnostics of linear regression model
`plotEffects`	Plot main effects of predictors in linear regression model
`plotInteraction`	Plot interaction effects of two predictors in linear regression model
`plotPartialDependence`	Create partial dependence plot (PDP) and individual conditional expectation (ICE) plots
`plotResiduals`	Plot residuals of linear regression model
`plotSlice`	Plot of slices through fitted linear regression surface

收集线性模型的属性

gather Gather properties of Statistics and Machine Learning Toolbox object from GPU

`RegressionLinear` 和 `RegressionPartitionedLinear` 函数

创建对象

fitrlinear Fit linear regression model to high-dimensional data

使用 `RegressionLinear` 对象

`predict`	Predict response of linear regression model
`lime`	Local interpretable model-agnostic explanations (LIME)
`loss`	Regression loss for linear regression models
`partialDependence`	Compute partial dependence
`plotPartialDependence`	Create partial dependence plot (PDP) and individual conditional expectation (ICE) plots
`shapley`	Shapley values
`selectModels`	Select fitted regularized linear regression models

使用 `RegressionPartitionedLinear` 对象

`kfoldLoss`	Regression loss for observations not used in training
`kfoldPredict`	Predict responses for observations not used for training

不使用对象的线性回归

拟合和计算线性回归

`dwtest`	Durbin-Watson test with residual inputs
`invpred`	Inverse prediction
`linhyptest`	Linear hypothesis test
`plsregress`	Partial least-squares (PLS) regression
`regress`	多元线性回归
`regstats`	Regression diagnostics
`relieff`	Rank importance of predictors using ReliefF or RReliefF algorithm
`robustfit`	Fit robust linear regression
`stepwisefit`	Fit linear regression model using stepwise regression

准备数据

`x2fx`	Convert predictor matrix to design matrix
`dummyvar`	Create dummy variables

交互式工具

`robustdemo`	Interactive robust regression
`rsmdemo`	Interactive response surface demonstration
`rstool`	Interactive response surface modeling
`stepwise`	Interactive stepwise regression

主题

线性回归简介

What Is a Linear Regression Model?

Regression models describe the relationship between a dependent variable and one or more independent variables.

Linear Regression

Fit a linear regression model and examine the result.

Stepwise Regression

In stepwise regression, predictors are automatically added to or trimmed from a model.

Reduce Outlier Effects Using Robust Regression

Fit a robust model that is less sensitive than ordinary least squares to large changes in small parts of the data.

Choose a Regression Function

Choose a regression function depending on the type of regression problem, and update legacy code using new fitting functions.

Summary of Output and Diagnostic Statistics

Evaluate a fitted model by using model properties and object functions.

Wilkinson Notation

Wilkinson notation provides a way to describe regression and repeated measures models without specifying coefficient values.

线性回归工作流

Linear Regression Workflow

Import and prepare data, fit a linear regression model, test and improve its quality, and share the model.

Interpret Linear Regression Results

Display and interpret linear regression output statistics.

Linear Regression with Interaction Effects

Construct and analyze a linear regression model with interaction effects and interpret the results.

Linear Regression Using Tables

This example shows how to perform linear and stepwise regression analyses using tables.

Linear Regression with Categorical Covariates

Perform a regression with categorical covariates using categorical arrays and fitlm.

Analyze Time Series Data

This example shows how to visualize and analyze time series data using a timeseries object and the regress function.

Train Linear Regression Model

Train a linear regression model using fitlm to analyze in-memory data and out-of-memory data.

偏最小二乘回归

Partial Least Squares

Partial least squares (PLS) constructs new predictor variables as linear combinations of the original predictor variables, while considering the observed response values, leading to a parsimonious model with reliable predictive power.

偏最小二乘回归和主成分回归

此示例说明如何应用偏最小二乘回归 (PLSR) 和主成分回归 (PCR)，并讨论这两种方法的有效性。当存在大量预测变量并且它们高度相关甚至共线时，PLSR 和 PCR 都可以作为建模响应变量的方法。这两种方法都将新的预测变量（称为成分）构建为原始预测变量的线性组合，但它们构建这些成分的方式不同。PCR 创建成分来解释在预测变量中观察到的变异性，而根本不考虑响应变量。而 PLSR 会考虑响应变量，因此常使模型能够拟合具有更少成分的响应变量。从实际应用上来说，这能否最终转化为更简约的模型要视情况而定。

多元线性回归

App

对象