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In machine learning, a linear regression model is a regression model that seeks to establish a linear relationship between a so-called explained variable and one or more so-called explanatory variables.

Also referred to as linear model or linear regression model.

Among the linear regression models, the simplest is the affine adjustment which consists in finding the straight line allowing to explain the behavior of a statistical variable y as being an affine function of another statistical variable x.

The linear regression model denotes a model in which the conditional expectation of y given x is an affine function of the parameters.

One can also consider models in which it is the conditional median of y knowing x or any quantile of the distribution of y knowing x which is an affine function of the parameters.

Simple linear regression

A simple linear model is generally called a linear regression model with a single explanatory variable.

This model is often presented as an affine adjustment model.

Multiple linear regression

As opposed to the simple linear regression model, the multiple linear regression model is defined as any linear regression model with at least two explanatory variables.