  We consider linear models where $d$ potential causes $X_1,...,X_d$ are
correlated with one target quantity $Y$ and propose a method to infer whether
the association is causal or whether it is an artifact caused by overfitting or
hidden common causes. We employ the idea that in the former case the vector of
regression coefficients has 'generic' orientation relative to the covariance
matrix $\Sigma_{XX}$ of $X$. Using an ICA based model for confounding, we show
that both confounding and overfitting yield regression vectors that concentrate
mainly in the space of low eigenvalues of $\Sigma_{XX}$.
