In reply to Charlie. Good to hear from you, Charlie. You are mathematically correct. Numerically, PROC REG uses the eigenvalue decomposition of the symmetric covariance or correlation matrix (as stated in the documentation), which is more efficient. You can derive the spectral (eigenvalue) decomposition from the SVD: If X = UDV` then X`X = VD`U`UDV`     = VD`DV` by orthogonality     = VQV` where Q=D*D is the matrix of eigenvalues. That proves the spectral decomposition. Because PROC REG has to compute the X`X matrix for regression, it uses that matrix for the collinearity diagnostics, too.