# Linear Regression

In statistics, linear regression is a linear approach to modeling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.

In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are estimated from the data. Such models are called linear models. Most commonly, the conditional mean of the response given the values of the explanatory variables (or predictors) is assumed to be an affine function of those values; less commonly, the conditional median or some other quantile is used. Like all forms of regression analysis, linear regression focuses on the conditional probability distribution of the response given the values of the predictors, rather than on the joint probability distribution of all of these variables, which is the domain of multivariate analysis.

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## Linear Regression

10 min
Beginner
Video
Theory

Linear regression is a cornerstone of data-driven modeling; here we show how the SVD can be used for linear regression.

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## Linear Regression 1 [Matlab]

12 min
Intermediate
Video
Application

This video describes how the singular value decomposition (SVD) can be used for linear regression in Matlab (part 1).

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## Least Squares Regression and the SVD

5 min
Beginner
Video
Theory

This video describes how the SVD can be used to solve linear systems of equations. In particular, it is possible to solve nonsquare systems (overdetermined or underdetermined) via least...

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## Linear Regression 3 [Python]

10 min
Intermediate
Video
Application

This video describes how the singular value decomposition (SVD) can be used for linear regression in Python (part 3).

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## Linear Regression 2 [Python]

5 min
Intermediate
Video
Application

This video describes how the singular value decomposition (SVD) can be used for linear regression in Python (part 2).

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## Linear Regression 1 [Python]

6 min
Intermediate
Video
Application

This video describes how the singular value decomposition (SVD) can be used for linear regression in Python (part 1).

See More