The Fritsch-Waugh-Lovell theorem: if y = ax + by + cz + (zero-mean nuisance), I can estimate a least-squares model of the form y' = ax + b*y + (zero-mean nui

The Fritsch-Waugh-Lovell theorem: if y = ax + by + cz + (zero-mean nuisance), I can estimate a least-squares model of the form y' = ax + b*y + (zero-mean nuisance) and get a correct estimate of b, as long as y and z are uncorrelated. (Where this breaks down: for example, a regression of IQ on age and arm length; omit age and you'll get longer arms (older kids) producing higher IQ scores, because age and arm length are correlated.)