A set arithmetic-based linear regression model for modelling interval-valued responses through real-valued variables

A new linear regression model for an interval-valued response and a real-valued explanatory variable is presented. The approach is based on the interval arithmetic. Comparisons with previous methods are discussed. The new linear model is theoretically analyzed and the regression parameters are estimated. Some properties of the regression estimators are investigated. Finally, the performance of the procedure is illustrated using both a real-life application and simulation studies.