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Math Help - Changes in the Regression Coefficient

  1. #1
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    Changes 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?
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  2. #2
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    Quote Originally Posted by motdepasse View Post
    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?
    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.
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