多重线性回归- MATLAB & Simulink

`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 (自 R2020b 起)

可视化线性模型和摘要统计量

`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 (自 R2020b 起)

`RegressionLinear` 和 `RegressionPartitionedLinear` 函数

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) (自 R2020b 起)
`loss`	Regression loss for linear regression models
`partialDependence`	Compute partial dependence (自 R2020b 起)
`plotPartialDependence`	Create partial dependence plot (PDP) and individual conditional expectation (ICE) plots
`shapley`	Shapley values (自 R2021a 起)
`selectModels`	Select fitted regularized linear regression models

使用 `RegressionPartitionedLinear` 对象

`kfoldLoss`	Regression loss for cross-validated linear regression model
`kfoldPredict`	Predict responses for observations in cross-validated linear regression model

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`	多重线性回归
`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

多项式曲线拟合

`polyconf`	Polynomial confidence intervals
`polyfit`	多项式曲线拟合

准备数据

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

交互式工具

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

`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

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.
- Predict Responses Using RegressionLinear Predict Block
  This example shows how to use the RegressionLinear Predict block for response prediction in Simulink®. (自 R2023a 起)
- Accelerate Linear Model Fitting on GPU
  This example shows how you can accelerate regression model fitting by running functions on a graphical processing unit (GPU).
  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
    应用偏最小二乘回归 (PLSR) 和主成分回归 (PCR)，并研究这两种方法的有效性。
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RegressionLinear Predict	使用线性回归模型预测响应 (自 R2023a 起)
IncrementalRegressionLinear Predict	Predict responses using incremental linear regression model (自 R2023b 起)
IncrementalRegressionLinear Fit	Fit incremental linear regression model (自 R2023b 起)
Update Metrics	Update performance metrics in incremental learning model given new data (自 R2023b 起)

LinearModel 和 CompactLinearModel 函数

创建 LinearModel 对象

创建 CompactLinearModel 对象