Residual and confidence interval for uncertain regression model with imprecise observations

摘要

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.