Regression and Random Confounding.

An ordinary least squares regression estimate for the slope, regardless of its strength, can have its sign reversed through adjustment for a random confounding vector of data. The assumption of a rotationally invariant distribution, on the space of centered, random, confounding vectors of data, makes calculation of probabilities for these reversals possible. Here, as the sample size increases, these probabilities are shown to decrease exponentially. This analytic result leads to some asymptotic comparison between regular sampling error and the error due to a mis-specified model. [ABSTRACT FROM AUTHOR]