## 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}`

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.

- Statistics Toolbox Overview 3:06 (Video)
- Fitting with MATLAB: Statistics, Optimization, and Curve Fitting 38:37 (Webinar)
- Partial Least Squares Regression and Principal Components Regression (Example)
- MATLAB Tools for Scientists - Introduction to Statistical Analysis 54:52 (Webinar)
- Machine Learning with MATLAB 3:02 (Video)
- Estimating Transfer Functions and Process Models 2:27 (Video)

- What Are Linear Regression Models? (Documentation)
- Linear Model Function in Statistics Toolbox (Function)
- Choosing a Fitting Method for Linear Regression (Documentation)
- Interpreting Results of a Linear Regression (Documentation)
- Analyzing Linear Regression Diagnostics (Documentation)
- What is Robust Regression? (Documentation)

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