Choose a Regression Function

Regression is the process of fitting models to data. The models must have numerical responses. For models with categorical responses, see Parametric Classification or Supervised Learning Workflow and Algorithms. The regression process depends on the model. If a model is parametric, regression estimates the parameters from the data. If a model is linear in the parameters, estimation is based on methods from linear algebra that minimize the norm of a residual vector. If a model is nonlinear in the parameters, estimation is based on search methods from optimization that minimize the norm of a residual vector.

This table describes which function to use depending on the type of regression problem.

Model Components	Result of Regression	Function to Use
Continuous or categorical predictors, continuous response, linear model	Fitted model coefficients	`fitlm`. See Linear Regression.
Continuous or categorical predictors, continuous response, linear model of unknown complexity	Fitted model and fitted coefficients	`stepwiselm`. See Stepwise Regression.
Continuous or categorical predictors, response possibly with restrictions such as nonnegative or integer-valued, generalized linear model	Fitted generalized linear model coefficients	`fitglm` or `stepwiseglm`. See Generalized Linear Models.
Continuous predictors with a continuous nonlinear response, parametrized nonlinear model	Fitted nonlinear model coefficients	`fitnlm`. See Nonlinear Regression.
Continuous predictors, continuous response, linear model	Set of models from ridge, lasso, or elastic net regression	`lasso` or `ridge`. See Lasso and Elastic Net or Ridge Regression.
Correlated continuous predictors, continuous response, linear model	Fitted model and fitted coefficients	`plsregress`. See Partial Least Squares.
Continuous or categorical predictors, continuous response, unknown model	Nonparametric model	`fitrtree` or `fitrensemble`.
Categorical predictors only	ANOVA	`anova`, `anova1`, `anova2`, `anovan`.
Continuous predictors, multivariable response, linear model	Fitted multivariate regression model coefficients	`mvregress`
Continuous predictors, continuous response, mixed-effects model	Fitted mixed-effects model coefficients	`nlmefit` or `nlmefitsa`. See Mixed-Effects Models.

Update Legacy Code with New Fitting Methods

There are several Statistics and Machine Learning Toolbox™ functions for performing regression. The following sections describe how to replace calls to older functions to new versions:

`regress` into `fitlm`

Previous Syntax:

[b,bint,r,rint,stats] = regress(y,X)

where X contains a column of ones.

Current Syntax:

mdl = fitlm(X,y)

where you do not add a column of ones to X.

Equivalent values of the previous outputs:

b — mdl.Coefficients.Estimate
bint — coefCI(mdl)
r — mdl.Residuals.Raw
rint — There is no exact equivalent. Try examining mdl.Residuals.Studentized to find outliers.
stats — mdl contains various properties that replace components of stats.

`regstats` into `fitlm`

Previous Syntax:

stats = regstats(y,X,model,whichstats)

Current Syntax:

mdl = fitlm(X,y,model)

Obtain statistics from the properties and methods of the LinearModel object (mdl). For example, see the mdl.Diagnostics and mdl.Residuals properties.

`robustfit` into `fitlm`

Previous Syntax:

[b,stats] = robustfit(X,y,wfun,tune,const)

Current Syntax:

mdl = fitlm(X,y,'robust','on') % bisquare

Or to use the wfun weight and the tune tuning parameter:

opt.RobustWgtFun = 'wfun';
opt.Tune = tune; % optional
mdl = fitlm(X,y,'robust',opt)

Obtain statistics from the properties and methods of the LinearModel object (mdl). For example, see the mdl.Diagnostics and mdl.Residuals properties.

`stepwisefit` into `stepwiselm`

Previous Syntax:

[b,se,pval,inmodel,stats,nextstep,history] = stepwisefit(X,y,Name,Value)

Current Syntax:

mdl = stepwiselm(ds,modelspec,Name,Value)

mdl = stepwiselm(X,y,modelspec,Name,Value)

Obtain statistics from the properties and methods of the LinearModel object (mdl). For example, see the mdl.Diagnostics and mdl.Residuals properties.

`glmfit` into `fitglm`

Previous Syntax:

[b,dev,stats] = glmfit(X,y,distr,param1,val1,...)

Current Syntax:

mdl = fitglm(X,y,distr,...)

Obtain statistics from the properties and methods of the GeneralizedLinearModel object (mdl). For example, the deviance is mdl.Deviance, and to compare mdl against a constant model, use devianceTest(mdl).

`nlinfit` into `fitnlm`

Previous Syntax:

[beta,r,J,COVB,mse] = nlinfit(X,y,fun,beta0,options)

Current Syntax:

mdl = fitnlm(X,y,fun,beta0,'Options',options)

Equivalent values of the previous outputs:

beta — mdl.Coefficients.Estimate
r — mdl.Residuals.Raw
covb — mdl.CoefficientCovariance
mse — mdl.mse

mdl does not provide the Jacobian (J) output. The primary purpose of J was to pass it into nlparci or nlpredci to obtain confidence intervals for the estimated coefficients (parameters) or predictions. Obtain those confidence intervals as:

parci = coefCI(mdl)
[pred,predci] = predict(mdl)