  It is well known that parameters for strongly correlated predictor variables
in a linear model cannot be accurately estimated. We look for linear
combinations of these parameters that can be. Under a uniform model, we find
such linear combinations in a neighborhood of a simple variability weighted
average of these parameters. Surprisingly, this variability weighted average is
more accurately estimated when the variables are more strongly correlated, and
it is the only linear combination with this property. It can be easily computed
for strongly correlated predictor variables in all linear models and has
applications in inference and estimation concerning parameters of such
variables.
