For anybody who's interested: perfect multicollinearity (which is rare, except in case of human oversight) causes a matrix of less-than-full rank, which essenti

For anybody who's interested: perfect multicollinearity (which is rare, except in case of human oversight) causes a matrix of less-than-full rank, which essentially means that it's not invertible (the matrix analog of "divide-by-zero" error). More commonly, you'll end up with imperfect multicollinearity, which means that two variables are almost the same, but slightly different. The danger with perfect multicollinearity is that (a) you'll end up with very high variances associated with those predictors, but furthermore (b) the predictor reported as being the 'strongest' may actually not be the strongest. In fact, it may not even be relevant; the model just "happens to be associating most of the variation in the response variable with that predictor. It's a more complicated version of this principle: http://xkcd.com/882/ http://xkcd.com/882/ I mention this because I see people - including people who should know better! - falling into this trap all the time. It's easy to overlook, particularly when you see the results you were expecting.