Your extra column is not redundant: it adds an extra column of
information, and outliers in that column after removing the effects of the
other columns are still multivariate outliers.
Effectively you have added one more dimension to the sphered point cloud,
and mahalanobis distance is Euclidea
Dear R-experts,
Searching the help archives I found a recommendation to do multivariate
outlier identification by mahalanobis distances based on a robustly estimated
covariance matrix and compare the resulting distances to a chi^2-distribution
with p (number of your variables) degrees of freedom
