Constrained linear regression models for interval-valued data with dependence

This paper introduces some approaches to fitting a constrained linear regression model to interval-valued data. The use of inequality constraints guarantee mathematical coherence between the predicted values of the lower bound (y circ_Li) and the upper bound (y circ_Ui). The authors also propose expressions to the goodness of fit measure called determination coefficient. The assessment of the proposed prediction methods is based on the average behaviour of the root mean square error and of the square of the correlation coefficient in the framework of a Monte Carlo experiment. The synthetic data sets takes into account the dependence or not between the midpoint and range of the intervals, among others aspects. Finally, the approaches are applied in a real data-set.