The Wolfram Language's symbolic architecture makes possible a uniquely convenient approach to working with statistical models. Starting from arbitrary data, the Wolfram Language generates symbolic representations of fitted models, from which a full spectrum of results and diagnostics can immediately be extracted, visualized, or used in other computations.

Fitting Framework

ModelFit — fit one or more models to data

ModelFitReport — model report with fit metrics and charts

Model Families

LinearModel — prediction as a linear function of features

DecisionTreeModel — a sequence of binary decisions on one feature at a time

ExponentialModel  ▪  LogModel  ▪  NearestModel  ▪  FormulaModel  ▪  PolynomialModel  ▪  PowerModel  ▪  PeriodicModel  ▪  PerceptronModel

Nonparametric Modeling

LocalModelFit — fit a local polynomial regression (LOESS) model to data

KernelModelFit — fit a local kernel regression model to data

Parametric Modeling

LinearModelFit — fit a linear regression model to data

NonlinearModelFit — fit a nonlinear regression model to data

GeneralizedLinearModelFit — generalized linear models, with general link functions

LogitModelFit  ▪  ProbitModelFit

Fitted Model Properties

FittedModel — symbolic representation of a model

"BestFit" — fitted function μ[x]

"BestFitAround" — fitted function and confidence bands Around[μ[x],σ_c[x]]

"BestFitDataAround" — fitted function and prediction bands Around[μ[x],σ_p[x]]

"BestFit"  ▪  "FitResiduals"  ▪  "ANOVA"  ▪  "ParameterEstimate"  ▪  "CookDistances"  ▪  "Deviances"  ▪  "AIC"  ▪  "FitCurvatureTable"  ▪  ...

Detailed Control

DesignMatrix — construct a design matrix from data

Weights  ▪  NominalVariables  ▪  LinkFunction  ▪  LinearOffsetFunction  ▪  FitDegree

ConfidenceLevel  ▪  VarianceEstimatorFunction  ▪  DispersionEstimatorFunction

Symbolic Model Discovery

FindFormula — try to find a simple symbolic formula for data

FindDistribution — try to find a simple symbolic form for the distribution of data