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

Marco Riani (), Anthony C. Atkinson, Gianluca Morelli and Aldo Corbellini
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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

Stats, 2025, vol. 8, issue 1, 1-30

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.

Keywords: AVAS; Box–Cox transformation; brushing; forward search; generalized additive model (GAM); linked plots (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2025
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