A Linear Regression Model for Interval-Valued Response Based on Set Arithmetic

Several linear regression models involving interval-valued variables have been formalized based on the interval arithmetic. In this work, a new linear regression model with interval-valued response and real predictor based on the interval arithmetic is formally described. The least-squares estimation of the model is solved by means of a constrained minimization problem which guarantees the coherency of the estimators with the regression parameters. The practical applicability of the estimation method is checked on a real-life example, and the empirical behaviour of the procedure is shown by means of some simulation studies.