  This paper discusses linear regression of strongly correlated data that
arises, for example, in magnetohydrodynamic equilibrium reconstructions. We
have proved that, generically, the covariance matrix of the estimated
regression parameters for fixed sample size goes to zero as the correlations
become unity. That is, in this limit the estimated parameters are known with
perfect accuracy. Simple examples are shown to illustrate this effect and the
nature of the exceptional cases in which the estimate covariance does not go to
zero.
