  It is clear that conventional statistical inference protocols need to be
revised to deal correctly with the high-dimensional data that are now common.
Most recent studies aimed at achieving this revision rely on powerful
approximation techniques, that call for rigorous results against which they can
be tested. In this context, the simplest case of high-dimensional linear
regression has acquired significant new relevance and attention. In this paper
we use the statistical physics perspective on inference to derive a number of
new exact results for linear regression in the high-dimensional regime.
