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The Use of Modern Robust Regression Analysis with Graphics: An Example from Marketing

Author

Listed:
  • Marco Riani

    (Dipartimento di Scienze Economiche e Aziendali and Interdepartmental Centre for Robust Statistics, Università di Parma, 43100 Parma, Italy)

  • Anthony C. Atkinson

    (The London School of Economics, London WC2A 2AE, UK)

  • Gianluca Morelli

    (Dipartimento di Scienze Economiche e Aziendali and Interdepartmental Centre for Robust Statistics, Università di Parma, 43100 Parma, Italy)

  • Aldo Corbellini

    (Dipartimento di Scienze Economiche e Aziendali and Interdepartmental Centre for Robust Statistics, Università di Parma, 43100 Parma, Italy)

Abstract

Routine least squares regression analyses may sometimes miss important aspects of data. To exemplify this point we analyse a set of 1171 observations from a questionnaire intended to illuminate the relationship between customer loyalty and perceptions of such factors as price and community outreach. Our analysis makes much use of graphics and data monitoring to provide a paradigmatic example of the use of modern robust statistical tools based on graphical interaction with data. We start with regression. We perform such an analysis and find significant regression on all factors. However, a variety of plots show that there are some unexplained features, which are not eliminated by response transformation. Accordingly, we turn to robust analyses, intended to give answers unaffected by the presence of data contamination. A robust analysis using a non-parametric model leads to the increased significance of transformations of the explanatory variables. These transformations provide improved insight into consumer behaviour. We provide suggestions for a structured approach to modern robust regression and give links to the software used for our data analyses.

Suggested Citation

  • Marco Riani & Anthony C. Atkinson & Gianluca Morelli & Aldo Corbellini, 2025. "The Use of Modern Robust Regression Analysis with Graphics: An Example from Marketing," Stats, MDPI, vol. 8(1), pages 1-30, January.
    • Handle: RePEc:gam:jstats:v:8:y:2025:i:1:p:6-:d:1562828
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    References listed on IDEAS

    as
    1. Riani, Marco & Atkinson, Anthony Curtis & Corbellini, Aldo & Farcomeni, Alessio & Laurini, Fabrizio, 2024. "Information Criteria for Outlier Detection Avoiding Arbitrary Significance Levels," Econometrics and Statistics, Elsevier, vol. 29(C), pages 189-205.
    2. D. R. Cox, 1992. "Causality: Some Statistical Aspects," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 155(2), pages 291-301, March.
    3. Jatinder Singh & Oriol Iglesias & Joan Batista-Foguet, 2012. "Does Having an Ethical Brand Matter? The Influence of Consumer Perceived Ethicality on Trust, Affect and Loyalty," Journal of Business Ethics, Springer, vol. 111(4), pages 541-549, December.
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