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What methods would you recommend for testing whether a variable Y is the weighted sum of n, not necessarily independent, variables? Only m < n of these variables are known.

The problem is easy if the variables are independent. (In my setting their co-variance is close to zero).

Yossi Gil
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  • Please add more information. Are we talking about an exact weighted sum or is there an error term? Are the two variables that sum up to Y observed? – Erik May 07 '12 at 06:45
  • Just edited the text to make my meaning clearer. – Yossi Gil May 07 '12 at 07:28

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Have you considered a multiple regression analysis with your m predictors and Y as the dependent variable? If so, why are you not comfortable with that approach? If not, would that be of help to you?

Joel W.
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  • My fear was the (weak) dependency. I noticed a detailed answer here: http://stats.stackexchange.com/questions/4517/regression-with-multiple-dependent-variables so, I guess my question is a duplicate. – Yossi Gil May 07 '12 at 13:38