  Several efforts have been done to bring ROC analysis beyond (binary)
classification, especially in regression. However, the mapping and
possibilities of these proposals do not correspond to what we expect from the
analysis of operating conditions, dominance, hybrid methods, etc. In this paper
we present a new representation of regression models in the so-called
regression ROC (RROC) space. The basic idea is to represent over-estimation on
the x axis and under-estimation on the y axis. The curves are just drawn by
adjusting a shift, a constant that is added (or subtracted) to the predictions,
and plays a similar role as a threshold in classification. From here, we
develop the notions of optimal operating condition, convexity, dominance, and
explore several evaluation metrics that can be shown graphically, such as the
area over the RROC curve (AOC). In particular, we show a novel and significant
result, the AOC is equal to the error variance (multiplied by a factor which
does not depend on the model). The derivation of RROC curves with non-constant
shifts and soft regression models, and the relation with cost plots is also
discussed.
