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Linear Regression

Encyclopedia of Machine Learning and Data Mining

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Definition

Linear regression is an instance of the Regression problem which is an approach to modeling a functional relationship between input variables x and an output/response variable y. In linear regression, a linear function of the input variables is used, and more generally a linear function of some vector function of the input variables ϕ(x) can also be used. The linear function estimates the mean of y (or more generally the median or a quantile).

Motivation and Background

Assume we are given a set of data points sampled from an underlying but unknown distribution, each of which includes input x and output y. The task of regression is to learn a hidden functional relationship between x and y from observed and possibly noisy data points, so y is to be approximated in some way by f(x). This is the task covered in more detail in Regression. A general approach to the problem is to make the function f() be linear. Depending on the optimization criteria used to fit between the linear...

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Notes

  1. 1.

    Statistical textbooks and machine learning textbooks, such as Bishop (2006) among others, introduce different linear regression models. For a large variety of built-in linear regression techniques,refer to R (http://www.r-project.org/).

Recommended Reading

Statistical textbooks and machine learning textbooks, such as Bishop (2006) among others, introduce different linear regression models. For a large variety of built-in linear regression techniques,refer to R (http://www.r-project.org/).

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  • Golub GH, Van Loan CF (1996) Matrix computations, 3rd edn. John Hopkins University Press, Baltimore

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  • Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in C: the art of scientific computing, 2nd edn. Cambridge University Press, Cambridge. ISBN:0-521-43108-5

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Author information

Authors and Affiliations

  1. SMiLe CLiNiC, Department of Informatics, University of Sussex, Falmer, East Sussex, UK

    Novi Quadrianto

  2. Faculty of Information Technology, Monash University, Clayton, VIC, Australia

    Wray L. Buntine

Authors
  1. Novi Quadrianto
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  2. Wray L. Buntine
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Corresponding author

Correspondence to Novi Quadrianto .

Editor information

Editors and Affiliations

  1. Engineering (CSE), University of New South Wales School of Computer Science &, Sydney, New South Wales, Australia

    Claude Sammut

  2. Software Engineering, Monash University School of Computer Science &, Melbourne, Victoria, Australia

    Geoffrey I. Webb

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Quadrianto, N., Buntine, W.L. (2016). Linear Regression. In: Sammut, C., Webb, G. (eds) Encyclopedia of Machine Learning and Data Mining. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7502-7_481-1

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  • DOI: https://doi.org/10.1007/978-1-4899-7502-7_481-1

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  • Online ISBN: 978-1-4899-7502-7

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Chapter history

  1. Latest

    Linear Regression
    Published:
    06 May 2023

    DOI: https://doi.org/10.1007/978-1-4899-7502-7_481-2

  2. Original

    Linear Regression
    Published:
    02 September 2016

    DOI: https://doi.org/10.1007/978-1-4899-7502-7_481-1

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