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Multiple Linear Regression

Linear regression with multiple predictor variables

For greater accuracy on low-dimensional through medium-dimensional data sets, fit a linear regression model using fitlm.

For reduced computation time on high-dimensional data sets, fit a linear regression model using fitrlinear.


Regression LearnerTrain regression models to predict data using supervised machine learning


LinearModelLinear regression model
CompactLinearModelCompact linear regression model
RegressionLinearLinear regression model for high-dimensional data
RegressionPartitionedLinearCross-validated linear regression model for high-dimensional data


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Create LinearModel Object

fitlmFit linear regression model
stepwiselmPerform stepwise regression

Create CompactLinearModel Object

compactCompact linear regression model

Add or Remove Terms from Linear Model

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

Predict Responses

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

Evaluate Linear Model

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

Visualize Linear Model and Summary Statistics

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

Gather Properties of Linear Model

gatherGather properties of Statistics and Machine Learning Toolbox object from GPU

Create Object

fitrlinearFit linear regression model to high-dimensional data

Work with RegressionLinear Object

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
selectModelsSelect fitted regularized linear regression models

Work with RegressionPartitionedLinear Object

kfoldLossRegression loss for observations not used in training
kfoldPredictPredict responses for observations not used for training

Fit and Evaluate Linear Regression

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

Prepare Data

x2fxConvert predictor matrix to design matrix
dummyvarCreate dummy variables

Interactive Tools

robustdemoInteractive robust regression
rsmdemoInteractive response surface demonstration
rstoolInteractive response surface modeling
stepwiseInteractive stepwise regression


Introduction to Linear Regression

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.

Linear Regression Workflows

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.

Partial Least Squares Regression

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.

Partial Least Squares Regression and Principal Components Regression

Apply partial least squares regression (PLSR) and principal components regression (PCR), and explore the effectiveness of the two methods.