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Hi all,

I am estimating a simple regression: Y = C(1) + C(2)*X (1)

Suppose I find that: X = X1 + X2

So that (1) can be rewritten as: Y = C(1) + C(3)*X1 + C(4)*X2 (2)

Now I am interested in investigating (but don't know how to, please help!):

1. Whether regressions (1) and (2) are the same, i.e. whether C(2) = C(3) + C(4)
My initial thoughts are (i) to set up a system, then use a Wald test, or (ii) to set up a new regression: Y = C(1) + C(2)*X + C(3)*X1 + C(4)*X2 and then use a Wald test. But I am really not sure if there are any problems with either approaches.

2. Whether decomposing X into X1 and X2 is better (or worse) in terms of explaining Y.

Thank you very much for any hints.

Hi all,

I am estimating a simple regression: Y = C(1) + C(2)*X (1)

Suppose I find that: X = X1 + X2

So that (1) can be rewritten as: Y = C(1) + C(3)*X1 + C(4)*X2 (2)

Just estimate this equation and test c(3)=c(4)

or (ii) to set up a new regression: Y = C(1) + C(2)*X + C(3)*X1 + C(4)*X2

You should try this. You'll probably find the results enlightening.