  This work gives a simultaneous analysis of both the ordinary least squares
estimator and the ridge regression estimator in the random design setting under
mild assumptions on the covariate/response distributions. In particular, the
analysis provides sharp results on the ``out-of-sample'' prediction error, as
opposed to the ``in-sample'' (fixed design) error. The analysis also reveals
the effect of errors in the estimated covariance structure, as well as the
effect of modeling errors, neither of which effects are present in the fixed
design setting. The proofs of the main results are based on a simple
decomposition lemma combined with concentration inequalities for random vectors
and matrices.
