Under what condition (or conditions if you think it necessary) would one observe no change in the regression coefficient (e.g., b-hat y on X1) for some variable when another variable is added to the regression equation?

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- March 1st 2011, 05:52 AMmotdepasseChanges in the Regression Coefficient
Under what condition (or conditions if you think it necessary) would one observe no change in the regression coefficient (e.g., b-hat y on X1) for some variable when another variable is added to the regression equation?

- March 1st 2011, 09:18 AMtheodds
If you have k predictors, X_1, X_2, ...., X_k that are mutually orthogonal and you add X_{k + 1} that is also orthogonal. My intuition says (i.e. I haven't worked it out myself) that this is sufficient and easy to show.

You may be able to get away with a less stringent condition that is the same in spirit (i.e. rooted in orthogonality) but the problem seems more difficult then.