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Combining Soft Computing and Statistical Methods in Data Analysis pp 263–271Cite as

A Linearity Test for a Simple Regression Model with LR Fuzzy Response

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Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 77))

Abstract

A linearity test for a simple regression model with an imprecise response is investigated. The values of the imprecise response are formalized through LR-fuzzy numbers, and the stochastic variability through probability spaces. The linear regression model and the least squares estimators of the regression parameters are briefly recalled. The nonparametric model to be employed as reference in the testing approach is also presented. The statistic compares the variability explained by the linear regression with the one explained by the nonparametric regression, since in case of linearity, both quantities should be similar. The problem is approached by bootstrapping. A simulation study has been carried out in order to check the performance of the procedure.

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Author information

Authors and Affiliations

  1. Dipartimento di Statistica, Prob. e Stat. Applicate - SAPIENZA, Università di Roma, 00185, Roma, Italy

    Maria Brigida Ferraro & Paolo Giordani

  2. Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, 33007, Oviedo, Spain

    Ana Colubi

Authors
  1. Maria Brigida Ferraro
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  2. Ana Colubi
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  3. Paolo Giordani
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Editor information

Editors and Affiliations

  1. Research Unit on Intelligent Data Analysis and Graphical Models, European Centre for Soft Computing Edificio Científico-Tecnológico. 3a Planta, C/ Gonzalo Gutiérrez Quirós s/n, 33600, Mieres, Spain

    Christian Borgelt , Gil González-Rodríguez  & Wolfgang Trutschnig ,  & 

  2. Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, Facultad de Ciencias, C/ Calvo Sotelo s/n, 33007, Oviedo, Spain

    María Asunción Lubiano

  3. Departamento de Estadística e I.O. yD.M., Universidad de Oviedo, Facultad de Ciencias, C/ Calvo Sotelo s/n, 33007, Oviedo, Spain

    María Ángeles Gil

  4. Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447, Warsaw, Poland

    Przemysław Grzegorzewski

  5. Systems Research Institute, Polish Academy of Science, Newelska 6, 01-447, Warsaw, Poland

    Olgierd Hryniewicz

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© 2010 Springer-Verlag Berlin Heidelberg

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Ferraro, M.B., Colubi, A., Giordani, P. (2010). A Linearity Test for a Simple Regression Model with LR Fuzzy Response. In: Borgelt, C., et al. Combining Soft Computing and Statistical Methods in Data Analysis. Advances in Intelligent and Soft Computing, vol 77. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14746-3_33

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  • DOI: https://doi.org/10.1007/978-3-642-14746-3_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14745-6

  • Online ISBN: 978-3-642-14746-3

  • eBook Packages: EngineeringEngineering (R0)

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