  Interval-valued linear regression has been investigated for some time. One of
the critical issues is optimizing the balance between model flexibility and
interpretability. This paper proposes a linear model for interval-valued data
based on the affine operators in the cone $\mathcal{C} = \{ (x, y) \in
\mathbb{R}^2 | x \leq y\}$. The resulting new model is shown to have improved
flexibility over typical models in the literature, while maintaining a good
interpretability. The least squares (LS) estimators of the model parameters are
provided in a simple explicit form, which possesses a series of nice
properties. Further investigations into the LS estimators shed light on the
positive restrictions of a subset of the parameters and their implications on
the model validity. A simulation study is presented that supports the
theoretical findings. An application to a real data set is also provided to
demonstrate the applicability of our model.
