A friend asked me this question to which I cannot answer: he is running a linear regression and he has 3 categorical independent variables which, if used altogether, would give multicollinearity. If he uses the first and the second dummies in the linear regression he obtains significant coefficients. If instead he uses the second and the third dummies he does not.
How can this be possible? Shouldn't the information contained in any of the two dummies be the same? Maybe there is a mistake elsewhere.