Linear Model

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Describe mathematical relationships and make predictions from experimental data

Linear models describe a continuous response variable as a function of one or more predictor variables. They can help you understand and predict the behavior of complex systems or analyze experimental, financial, and biological data.

Linear regression is a statistical method used to create a linear model. The model describes the relationship between a dependent variable y (also called the response) as a function of one or more independent variables Xi (called the predictors). The general equation for a linear model is:

y = β0 + ∑ βiXi + εi

y = β 0 +   β i X i + ε i

where β represents linear parameter estimates to be computed and ε represents the error terms.

There are several types of linear regression:

  • Simple linear regression: models using only one predictor
  • Multiple linear regression: models using multiple predictors
  • Multivariate linear regression: models for multiple response variables

Simple linear regression is commonly done in MATLAB. For multiple and multivariate linear regression, see Statistics Toolbox. It enables stepwise, robust, and multivariate regression to:

  • Generate predictions
  • Compare linear model fits
  • Plot residuals
  • Evaluate goodness-of-fit
  • Detect outliers

To create a linear model that fits curves and surfaces to your data, see Curve Fitting Toolbox. To create linear models of dynamic systems from measured input-output data, see System Identification Toolbox. To create a linear model for control system design from a nonlinear Simulink model, see Simulink Control Design.

Examples and How To

Software Reference

See also: Statistics Toolbox, Curve Fitting Toolbox, machine learning, linearization, data fitting, data analysis, mathematical modeling, time series regression, linear model videos