Error bounds for computed least squares estimators

This paper is concerned with normwise errors in the LS estimation for linear regression. It provides probabilistic tail bounds for the normwise error between the computed least squares estimator and the parameter vector, when the least squares problem is solved in floating point arithmetic using either the normal equations method or a backward stable method (for example, using the Householder QR factorization or the singular value decomposition). These bounds are used to provide a condition under which the computationally more efficient normal equations method can safely be used instead of a backward stable method, without any loss of accuracy in the computed estimator.