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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 (Machine 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.

You have: | You want: | Use this: |
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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 ridgeSee Lasso and Elastic Net or Ridge Regression. |

Correlated continuous predictors, continuous response, linear model | Fitted model and fitted coefficients | plsregressSee Partial Least Squares. |

Continuous or categorical predictors, continuous response, unknown model | Nonparametric model | fitrtree or fitensembleSee Classification Trees and Regression Trees or Ensemble Methods. |

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 nlmefitsaSee Mixed-Effects Models. |

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

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

where `X` contains a column of ones.

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`.

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

mdl = fitlm(X,y,model)

Obtain statistics from the properties and methods of `mdl`. For example, see
the `mdl.Diagnostics` and `mdl.Residuals` properties.

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

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

Or to use the * wfun* weight and the

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

Obtain statistics from the properties and methods of `mdl`. For example, see
the `mdl.Diagnostics` and `mdl.Residuals` properties.

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

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

or

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

Obtain statistics from the properties and methods of `mdl`. For example, see
the `mdl.Diagnostics` and `mdl.Residuals` properties.

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

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

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

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

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)

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