多重线性回归

具有多个预测变量的线性回归

在一个多重线性回归模型中，响应变量取决于多个预测变量。您可以使用或不使用 LinearModel 对象来执行多重线性回归，也可以使用回归学习器来执行多重线性回归。

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

回归学习器使用有监督机器学习训练回归模型来预测数据

模块

RegressionLinear Predict使用线性回归模型预测响应 (自 R2023a 起)
IncrementalRegressionLinear PredictPredict responses using incremental linear regression model (自 R2023b 起)
IncrementalRegressionLinear FitFit incremental linear regression model (自 R2023b 起)
Detect DriftUpdate drift detector states and drift status with new data (自 R2024b 起)
Per Observation LossPer observation regression or classification error of incremental model (自 R2025a 起)
Update MetricsUpdate performance metrics in incremental learning model given new data (自 R2023b 起)

函数

全部展开

创建 LinearModel 对象

fitlm拟合线性回归模型
stepwiselmPerform stepwise regression

创建 CompactLinearModel 对象

compactCompact linear regression model

添加或删除线性模型中的项

addTermsAdd terms to linear regression model
removeTermsRemove terms from linear regression model
stepImprove linear regression model by adding or removing terms

预测响应

fevalPredict responses of linear regression model using one input for each predictor
predictPredict responses of linear regression model
randomSimulate responses with random noise for linear regression model

计算线性模型

anovaAnalysis of variance for linear regression model
coefCIConfidence intervals of coefficient estimates of linear regression model
coefTestLinear hypothesis test on linear regression model coefficients
dwtestDurbin-Watson test with linear regression model object
partialDependenceCompute partial dependence

可视化线性模型和摘要统计量

plotScatter plot or added variable plot of linear regression model
plotAddedAdded variable plot of linear regression model
plotAdjustedResponseAdjusted response plot of linear regression model
plotDiagnosticsPlot observation diagnostics of linear regression model
plotEffectsPlot main effects of predictors in linear regression model
plotInteractionPlot interaction effects of two predictors in linear regression model
plotPartialDependenceCreate partial dependence plot (PDP) and individual conditional expectation (ICE) plots
plotResidualsPlot residuals of linear regression model
plotSlicePlot of slices through fitted linear regression surface

收集线性模型的属性

gatherGather properties of Statistics and Machine Learning Toolbox object from GPU

创建 CensoredLinearModel 对象

fitlmcensFit censored linear regression model (自 R2025a 起)

创建 CompactCensoredLinearModel 对象

compactCreate compact censored linear regression model (自 R2025a 起)

预测响应

fevalPredict responses of censored linear regression model using one input for each predictor (自 R2025a 起)
predictPredict responses of censored linear regression model (自 R2025a 起)
randomSimulate responses with random noise for censored linear regression model (自 R2025a 起)

计算删失线性模型

coefCIConfidence intervals of coefficient estimates for censored linear regression model (自 R2025a 起)
coefTestLinear hypothesis test on censored linear regression model coefficients (自 R2025a 起)
partialDependenceCompute partial dependence

可视化删失线性模型和摘要统计量

plotPartialDependenceCreate partial dependence plot (PDP) and individual conditional expectation (ICE) plots
plotResidualsPlot residuals of censored linear regression model (自 R2025a 起)
plotSlicePlot of slices through fitted censored linear regression surface (自 R2025a 起)

创建对象

fitrlinearFit linear regression model to high-dimensional data

使用 RegressionLinear 对象

predictPredict response of linear regression model
limeLocal interpretable model-agnostic explanations (LIME)
lossRegression loss for linear regression models
partialDependenceCompute partial dependence
plotPartialDependenceCreate partial dependence plot (PDP) and individual conditional expectation (ICE) plots
shapleyShapley values (自 R2021a 起)
selectModelsSelect fitted regularized linear regression models

使用 RegressionPartitionedLinear 对象

kfoldLossRegression loss for cross-validated linear regression model
kfoldPredictPredict responses for observations in cross-validated linear regression model

创建对象

fitrqlinearTrain quantile linear regression model (自 R2024b 起)
compactReduce size of machine learning model
crossvalCross-validate machine learning model

使用 RegressionQuantileLinear 或 CompactRegressionQuantileLinear 对象

lossLoss for quantile linear regression model (自 R2024b 起)
predictPredict response for quantile linear regression model (自 R2024b 起)

使用 RegressionPartitionedQuantileModel 对象

kfoldLossLoss for cross-validated partitioned quantile regression model (自 R2025a 起)
kfoldPredictPredict responses for observations in cross-validated quantile regression model (自 R2025a 起)
kfoldfunCross-validate function for quantile regression (自 R2025a 起)

拟合和计算线性回归

dwtestDurbin-Watson test with residual inputs
invpredInverse prediction
linhyptestLinear hypothesis test
plsregressPartial least-squares (PLS) regression
regress多重线性回归
regstatsRegression diagnostics
relieffRank importance of predictors using ReliefF or RReliefF algorithm
robustfitFit robust linear regression
stepwisefitFit linear regression model using stepwise regression

多项式曲线拟合

polyconfPolynomial confidence intervals
polyfit多项式曲线拟合

准备数据

x2fxConvert predictor matrix to design matrix
dummyvarCreate dummy variables

交互式工具

polytoolInteractive polynomial fitting
robustdemoInteractive robust regression
rsmdemoInteractive response surface demonstration
rstoolInteractive response surface modeling
stepwiseInteractive stepwise regression

对象

LinearModelLinear regression model
CompactLinearModelCompact linear regression model
CensoredLinearModelCensored linear regression model (自 R2025a 起)
CompactCensoredLinearModelCompact censored linear regression model (自 R2025a 起)
RegressionLinearLinear regression model for high-dimensional data
RegressionPartitionedLinearCross-validated linear regression model for high-dimensional data
RegressionQuantileLinearQuantile linear regression model (自 R2024b 起)
CompactRegressionQuantileLinearCompact quantile linear regression model (自 R2025a 起)
RegressionPartitionedQuantileModelCross-validated quantile model for regression (自 R2025a 起)

主题

线性回归简介

线性回归工作流

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。