A new method to fit a linear regression model for interval-valued data

This paper introduces a new approach to fit a linear regression model on interval-valued data. Each example of the learning set is described by a feature vector where each feature value is an interval. In the proposed approach, it is fitted two linear regression models, respectively, on the mid-point and range of the interval values assumed by the variables on the learning set. The prediction of the lower and upper bound of the interval value of the dependent variable is accomplished from its mid-point and range which are estimated from the fitted linear regression models applied to the mid-point and range of each interval values of the independent variables. The evaluation of the proposed prediction method is based on the estimation of the average behaviour of root mean squared error and of the determination coefficient in the framework of a Monte Carlo experience in comparison with the method proposed by Billard and Diday [3].