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Thread: Hypotheses testing if R=1

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    Re: Hypotheses testing if R=1




    I believe, it has been several years since I read this, that when Y is a perfect linear combination of X there is perfect (not high) collinearity. It is impossible to generate a solution when this occurs so the software can not generate an answer.
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Hypotheses testing if R=1

    Quote Originally Posted by noetsi View Post
    I believe, it has been several years since I read this, that when Y is a perfect linear combination of X there is perfect (not high) collinearity. It is impossible to generate a solution when this occurs so the software can not generate an answer.
    Incorrect. You can fit the model but you can't do inference.
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    Re: Hypotheses testing if R=1

    Quote Originally Posted by rogojel View Post
    hi,
    just my five cents:
    your equation is precisely Y=x1+x2+x3 with all coefficients being 1 and no random term. The least squares is just not the right mathematical model, imho. From the equation point of view all terms have the same contribution.

    Now, in reality it could happen that x1 is generally higher then x3, for instance. This would be a simple ANOVA type of question and has nothing to do with the fact that the 3 xs are bound together in such an equation.

    regards
    rogojel
    That makes sense! Thank you!

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    Re: Hypotheses testing if R=1

    This is what John Fox says about perfect collinearity (you can find similar comments in other books).

    "Thus...[if perfect collinearity exists] than the denominators of b1 and b2 in Equation 3.2 is zero and these coefficients [the slopes] are undefined. More properly, there is an infinity of pairs of values of b1 and b2 that satisfy the normal equation." p 10 in Regression Diagnostics

    SAS will not even run when this occurs. SPSS gives an error message
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Hypotheses testing if R=1

    Note that in this case all of the predictors are linearly independent of one another so we don't fall into that particular case. We don't have perfect collinearity among the predictors.
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    Re: Hypotheses testing if R=1

    My appology. I did not see the OP say the IV are independent of each other
    "Very few theories have been abandoned because they were found to be invalid on the basis of empirical evidence...." Spanos, 1995

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    Re: Hypotheses testing if R=1


    We don't know for sure that they are independent without testing.
    Stop cowardice, ban guns!

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