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

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....

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Main Authors: Marco Riani, Anthony C. Atkinson, Gianluca Morelli, Aldo Corbellini
Format: Article
Language:English
Published: MDPI AG 2025-01-01
Series:Stats
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Online Access:https://www.mdpi.com/2571-905X/8/1/6
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author Marco Riani
Anthony C. Atkinson
Gianluca Morelli
Aldo Corbellini
author_facet Marco Riani
Anthony C. Atkinson
Gianluca Morelli
Aldo Corbellini
author_sort Marco Riani
collection DOAJ
description 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.
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spelling doaj-art-825ff37f4a4c4e6591d66f20f342125c2025-08-20T01:48:54ZengMDPI AGStats2571-905X2025-01-0181610.3390/stats8010006The Use of Modern Robust Regression Analysis with Graphics: An Example from MarketingMarco Riani0Anthony C. Atkinson1Gianluca Morelli2Aldo Corbellini3Dipartimento di Scienze Economiche e Aziendali and Interdepartmental Centre for Robust Statistics, Università di Parma, 43100 Parma, ItalyThe London School of Economics, London WC2A 2AE, UKDipartimento di Scienze Economiche e Aziendali and Interdepartmental Centre for Robust Statistics, Università di Parma, 43100 Parma, ItalyDipartimento di Scienze Economiche e Aziendali and Interdepartmental Centre for Robust Statistics, Università di Parma, 43100 Parma, ItalyRoutine 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.https://www.mdpi.com/2571-905X/8/1/6AVASBox–Cox transformationbrushingforward searchgeneralized additive model (GAM)linked plots
spellingShingle Marco Riani
Anthony C. Atkinson
Gianluca Morelli
Aldo Corbellini
The Use of Modern Robust Regression Analysis with Graphics: An Example from Marketing
Stats
AVAS
Box–Cox transformation
brushing
forward search
generalized additive model (GAM)
linked plots
title The Use of Modern Robust Regression Analysis with Graphics: An Example from Marketing
title_full The Use of Modern Robust Regression Analysis with Graphics: An Example from Marketing
title_fullStr The Use of Modern Robust Regression Analysis with Graphics: An Example from Marketing
title_full_unstemmed The Use of Modern Robust Regression Analysis with Graphics: An Example from Marketing
title_short The Use of Modern Robust Regression Analysis with Graphics: An Example from Marketing
title_sort use of modern robust regression analysis with graphics an example from marketing
topic AVAS
Box–Cox transformation
brushing
forward search
generalized additive model (GAM)
linked plots
url https://www.mdpi.com/2571-905X/8/1/6
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