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Linear Regression

Encyclopedia of Machine Learning and Data Science

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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 Ï•(x) can also be used. The linear function estimates the mean of y (or more generally the median or a quantile).

Motivation and Background

A set of data points sampled from an underlying but unknown distribution is assumed to be given. Each data point consists of input \(x\in \mathbb {R}^{d}\) and output \(y\in \mathbb {R}\). 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...

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Author information

Authors and Affiliations

  1. PAL Predictive Analytics Lab, University of Sussex, Brighton, UK

    Novi Quadrianto

  2. BCAM Severo Ochoa Strategic Lab on Trustworthy Machine Learning, Bilbao, Spain

    Novi Quadrianto

  3. College of Engineering & Computer Science, VinUniversity, Hanoi, Vietnam

    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. Clayton, VIC, Australia

    Dinh Phung

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

    Geoffrey I. Webb

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

    Claude Sammut

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Quadrianto, N., Buntine, W.L. (2023). Linear Regression. In: Phung, D., Webb, G.I., Sammut, C. (eds) Encyclopedia of Machine Learning and Data Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4899-7502-7_481-2

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

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4899-7502-7

  • Online ISBN: 978-1-4899-7502-7

  • eBook Packages: Springer Reference Computer SciencesReference Module Computer Science and Engineering

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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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