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Regression Analysis and Its Development

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A Mathematical Approach to Research Problems of Science and Technology

Part of the book series: Mathematics for Industry ((MFI,volume 5))

Abstract

Regression analysis aims to predict a target variable statistically by using explanatory variables. The analysis has a long history and is utilized in various situations. We will review linear regression analysis and describe model assessment methods based on the coefficient of determination and Akaike information criterion (AIC). Furthermore, we propose a relative coefficient of determination based on AIC for general statistical modeling. Finally, we illustrate variable selection and discuss recent developments in regression analysis.

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Author information

Authors and Affiliations

  1. Institute of Mathematics for Industry, Kyushu University, 744, Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

    Ryuei Nishii

Authors
  1. Ryuei Nishii
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Correspondence to Ryuei Nishii .

Editor information

Editors and Affiliations

  1. Kyushu University, Fukuoka, Japan

    Ryuei Nishii

  2. Department of Mathematics, Hokkaido University, Sapporo, Japan

    Shin-ichiro Ei

  3. Kyushu University Institute of Mathematics for Industry, Fukuoka, Japan

    Miyuki Koiso

  4. Kyushu University Institute of Mathematics for Industry, Fukuoka, Japan

    Hiroyuki Ochiai

  5. Kyushu University Institute of Mathematics for Industry, Fukuoka, Japan

    Kanzo Okada

  6. Faculty of Arts and Science, Kyushu University, Fukuoka, Japan

    Shingo Saito

  7. Kyushu University Institute of Mathematics for Industry, Fukuoka, Japan

    Tomoyuki Shirai

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© 2014 Springer Japan

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Nishii, R. (2014). Regression Analysis and Its Development. In: Nishii, R., et al. A Mathematical Approach to Research Problems of Science and Technology. Mathematics for Industry, vol 5. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55060-0_19

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  • DOI: https://doi.org/10.1007/978-4-431-55060-0_19

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  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-55059-4

  • Online ISBN: 978-4-431-55060-0

  • eBook Packages: EngineeringEngineering (R0)

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