st: SE of linear prediction: Use only SE of slope coefficient(s), or also that of the constant?

[Jen Zhen <jenzhen99@gmail.com>]

Dear listers,

I have estimated   Y = A + (B1*X1 + B2*X2 + B3*X3) + (C1*Z1 + C2*Z2+C3*Z3)+eps.

The X are a set of mutually exclusive dummies, and the Z are another
set of mutually exclusive dummies.

Now I want to use these estimated coefficients to compute the average
Y for the three different X cases, keeping Z fixed at any one of its
values, for simplicity say when all Z are zero.

I do this simply by computing    A+B1, and similarly for the other
constellations of X.

But I'm unsure what the correct standard error for this is:
Can I simply take the standard error of B1, or do I need also need to
add that of the constant A, as well as the covariance between the
estimated coefficients A and B1?

Many thanks,
JZ
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