# Multiple Linear Regression

Linear regression with multiple predictor variables

In a multiple linear regression model, the response variable depends on
more than one predictor variable. You can perform multiple linear regression
with or without the `LinearModel`

object, or by using the
**Regression Learner** app.

For greater accuracy on low-dimensional through medium-dimensional data sets, fit a linear regression model using `fitlm`

.

For reduced computation time on high-dimensional data sets, fit a linear regression model using `fitrlinear`

.

## Apps

Regression Learner | Train regression models to predict data using supervised machine learning |

## Blocks

RegressionLinear Predict | Predict responses using linear regression model |

## Functions

## Objects

`LinearModel` | Linear regression model |

`CompactLinearModel` | Compact linear regression model |

`RegressionLinear` | Linear regression model for high-dimensional data |

`RegressionPartitionedLinear` | Cross-validated linear regression model for high-dimensional data |

## Topics

### Introduction to Linear Regression

**What Is a Linear Regression Model?**

Regression models describe the relationship between a dependent variable and one or more independent variables.**Linear Regression**

Fit a linear regression model and examine the result.**Stepwise Regression**

In stepwise regression, predictors are automatically added to or trimmed from a model.**Reduce Outlier Effects Using Robust Regression**

Fit a robust model that is less sensitive than ordinary least squares to large changes in small parts of the data.**Choose a Regression Function**

Choose a regression function depending on the type of regression problem, and update legacy code using new fitting functions.**Summary of Output and Diagnostic Statistics**

Evaluate a fitted model by using model properties and object functions.**Wilkinson Notation**

Wilkinson notation provides a way to describe regression and repeated measures models without specifying coefficient values.

### Linear Regression Workflows

**Linear Regression Workflow**

Import and prepare data, fit a linear regression model, test and improve its quality, and share the model.**Interpret Linear Regression Results**

Display and interpret linear regression output statistics.**Linear Regression with Interaction Effects**

Construct and analyze a linear regression model with interaction effects and interpret the results.**Linear Regression Using Tables**

This example shows how to perform linear and stepwise regression analyses using tables.**Linear Regression with Categorical Covariates**

Perform a regression with categorical covariates using categorical arrays and`fitlm`

.**Analyze Time Series Data**

This example shows how to visualize and analyze time series data using a`timeseries`

object and the`regress`

function.**Train Linear Regression Model**

Train a linear regression model using`fitlm`

to analyze in-memory data and out-of-memory data.**Predict Responses Using RegressionLinear Predict Block**

This example shows how to use the RegressionLinear Predict block for response prediction in Simulink®.**Accelerate Linear Model Fitting on GPU**

This example shows how you can accelerate regression model fitting by running functions on a graphical processing unit (GPU).

### Partial Least Squares Regression

**Partial Least Squares**

Partial least squares (PLS) constructs new predictor variables as linear combinations of the original predictor variables, while considering the observed response values, leading to a parsimonious model with reliable predictive power.**Partial Least Squares Regression and Principal Components Regression**

Apply partial least squares regression (PLSR) and principal components regression (PCR), and explore the effectiveness of the two methods.