What Is a 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:
\[y = \beta_0 + \sum \ \beta_i X_i + \epsilon_i\]
where \(\beta\) represents linear parameter estimates to be computed and \(\epsilon\) 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
- 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
See also: Statistics and Machine Learning Toolbox, Curve Fitting Toolbox, machine learning, linearization, data fitting, data analysis, mathematical modeling, time series regression, linear model videos, Machine Learning Models, MANOVA