Residual and confidence interval for uncertain regression model with imprecise observations

Article type: Research Article

Authors: Lio, Waichon | Liu, Baoding^{; *}

Affiliations: Department of Mathematical Sciences, Tsinghua University, Beijing, China

Correspondence: [*] Corresponding author. Baoding Liu, Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China. Tel.: +86 01062787724; E-mail: liu@tsinghua.edu.cn.

Abstract: Regression model is a powerful analytical tool for estimating the relationships between explanatory variables and the response variable. Traditionally, it is often assumed that the data are observed precisely and characterized by crisp values. However, in many cases, those data are collected in an imprecise way and characterized in terms of uncertain variables. In this paper, the residual analysis of uncertain regression models is provided. Furthermore, an approach to obtain the forecast value and the confidence interval of the response variable for the new explanatory variables is given. Finally, a numerical example of the uncertain regression model is documented.

Keywords: Regression analysis, uncertainty theory, uncertain variable, residual, confidence interval

DOI: 10.3233/JIFS-18353

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 2, pp. 2573-2583, 2018