🚀 go-pugleaf

 Collinearity
The recent mention of condition numbers spurs me to amplify my earlier remarks.
 A covariance matrix might be very ill-conditioned in, say, having its smallest
eigenvalue be only 1/10000 times its largest eigenvalue.  But if we think of
the "predictors" in a regression as divided into "independent variables" and
"covariates", and you're mainly interested in estimating the effects of the
former on the dependent variable Y, and the collinearity is primarily among the
covariates, then you can have acceptably small standard errors where you need
them, despite extremely poor conditioning.  I suggest emphasizing tolerances
over condition numbers; and you look at only those tolerances that are
important to you.  Conditioning is usually important only if it's so bad that
it introduces rounding errors as opposed to sampling errors, and a good
regression program should warn you automatically if it's that bad.