A colleague asked me about some results with logistic regression. He had
two predictors of a binary outcome, call them A and B. When used alone,
predictor A was significantly related to the outcome and predictor B was
not. Moreover, the correlation between A and B was zero. When the
outcome was regressed on the two predictors simultaneously using logistic
regression both were significantly related to the outcome. In effect, the
coefficient for predictor B became larger. However, when OLS regression
was used instead, the coefficients for each predictor were the same as
when entered alone, which is what one would expect.
To elaborate a bit on my last answer - in OLS, the variance of y is
the variance of y, i.e. it doesn't matter whether y is regressed on
X1, or X1 and X2, or X1 and X2 and X3 - the variance of y will be the
same in every case.