Multivariate uncertain regression model with imprecise observations

The multivariate regression model is a mathematical tool for estimating the relationships among some explanatory variables and some response variables. In some cases, observed data are imprecise. In order to model those imprecise data, we can employ uncertainty theory to design the uncertain regression model by regarding those data as uncertain variables. Parameters estimation is an important topic in the uncertain regression model. In this paper, we explore a method of parameters estimation by the principle of least squares in the multivariate uncertain regression model containing more than one response variables and assuming both explanatory variables and response variables as uncertain variables. Besides, when the new explanatory variables are given, we propose an approach to obtain the forecast value and the confidence interval of the response variables. At last, a numerical example of the multivariate uncertain regression model is showed.