Off the beaten track: A new linear model for interval data

•A new linear regression model for interval data is presented.•The Interval Distributional regression model allows predicting an interval.•A method that takes in consideration the distribution within the intervals.•The range of time of unemployment for user-defined sociological classes was predicted.•Prediction for the burned area of forest fires was obtained with symbolic methods. We propose a new linear regression model for interval-valued variables. The model uses quantile functions to represent the intervals, thereby considering the distributions within them. In this paper we study the special case where the Uniform distribution is assumed in each observed interval, and we analyze the extension to the Symmetric Triangular distribution. The parameters of the model are obtained solving a constrained quadratic optimization problem that uses the Mallows distance between quantile functions. As in the classical case, a goodness-of-fit measure is deduced. Two applications on up-to-date fields are presented: one predicting duration of unemployment and the other allowing forecasting burned area by forest fires.