Linear Model |
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 X_{i} (called the predictors). The general equation for a linear model is:
y = β_{0} + ∑ β_{i}X_{i} + ε_{i}
$$\mathit{}\mathrm{}\mathrm{y}=\mathrm{\beta}{}_{0}+\mathrm{\sum}\mathrm{}\mathrm{\beta}{}_{i}\mathrm{X}{}_{i}+\mathrm{\epsilon}{}_{i}$$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 is commonly done in MATLAB. For multiple and multivariate linear regression, see Statistics Toolbox. It enables stepwise, robust, and multivariate regression to:
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.
See also: Statistics Toolbox, Curve Fitting Toolbox, machine learning, linearization, data fitting, data analysis, mathematical modeling, time series regression, linear model videos