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

Methodology