We study some problems in interval arithmetic treated in Kreinovich et al. [6]. First, we consider the best linear approximation of a quadratic interval function. Known to be NP-hard in the Turing model, we analyze its complexity in the real number model and the analoguous class NP _ℝ. We give new upper complexity bounds by locating the decision version in DS²_\mathbbR{D\Sigma^2_{{\mathbb{R}}}} (a real analogue of Σ²) and solve a problem left open in [6].