A multiple linear regression model for LR fuzzy random variables

In standard regression analysis the relationship between one (response) variable and a set of (explanatory) variables is investigated. In a classical framework the response is affected by probabilistic uncertainty (randomness) and, thus, treated as a random variable. However, the data can also be subjected to other kinds of uncertainty, such as imprecision. A possible way to manage all of these uncertainties is represented by the concept of fuzzy random variable (FRV). The most common class of FRVs is the LR family (LR FRV), which allows us to express every FRV in terms of three random variables, namely, the center, the left spread and the right spread. In this work, limiting our attention to the LR FRV class, we address the linear regression problem in presence of one or more imprecise random elements. The procedure for estimating the model parameters and the determination coefficient are discussed, and the hypothesis testing problem is addressed following a bootstrap approach. Furthermore, in order to illustrate how the proposed model works in practice, the results of a real-life example are given.