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It has been some time since interval-valued linear regression wasinvestigated. In this paper, we focus on linear regression for interval-valueddata within the framework of random sets. The model we propose generalizes aseries of existing models. We establish important properties of the model inthe space of compact convex subsets of $\mathbb{R}$, analogous to those for theclassical linear regression. Furthermore, we carry out theoreticalinvestigations into the least squares estimation that is widely used in theliterature. A simulation study is presented that supports our theorems.Finally, an application to a climate data set is provided to demonstrate theapplicability of our model.

On Linear Regression for Interval-valued Data in $\mathcal{K}_{\mathcal{C}}\left(\mathbb{R}\right)$