A Fuzzy-Statistical Tolerance Interval from Residuals of Crisp Linear Regression Models

Maryam Al-Kandari, Kingsley Adjenughwure and Kyriakos Papadopoulos
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Maryam Al-Kandari: Department of Mathematics, Kuwait University, P.O. Box 5969, Safat 13060, Khaldiyah City, Kuwait
Kingsley Adjenughwure: Department of Civil Engineering, Democritus University of Thrace, 67100 Xanthi, Greece
Kyriakos Papadopoulos: Department of Mathematics, Kuwait University, P.O. Box 5969, Safat 13060, Khaldiyah City, Kuwait

Mathematics, 2020, vol. 8, issue 9, 1-10

Abstract: Linear regression is a simple but powerful tool for prediction. However, it still suffers from some deficiencies, which are related to the assumptions made when using a model like normality of residuals, uncorrelated errors, where the mean of residuals should be zero. Sometimes these assumptions are violated or partially violated, thereby leading to uncertainties or unreliability in the predictions. This paper introduces a new method to account for uncertainty in the residuals of a linear regression model. First, the error in the estimation of the dependent variable is calculated and transformed to a fuzzy number, and this fuzzy error is then added to the original crisp prediction, thereby resulting in a fuzzy prediction. The results are compared to a fuzzy linear regression with crisp input and fuzzy output, in terms of their ability to represent uncertainty in prediction.

Keywords: tolerance interval; fuzzy linear regression; crisp linear regression; fuzzy-statistics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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