Re: how to determine the variance of dependant variable when all the var. of ind. variables r known in a linear relation


Old Mac User wrote:
Greg...

I think it would be nice if you would give this person the answer
without asking him/her to dig further into VAR(y) = E{ (y - E{y} )^2
}

IMHO, when a person comes to this board with a reasonable question...
expresses that question in "plain English"... then we should provide a
direct and practical answer without asking them to "learn all about
statistics".

Tutoring students who are attending courses for credit is one thing.
Helping someone with a simple question is another. As a consultant I'm
expected to "answer questions", not drive my clients to dig into
matters of little or no concern to them.

Full Disclosure: I'm a chemical engineer and also a statistician.

Something like...

Var(y) = (a^2) *Var(X1) + (b^2) * Var(X2)

assuming that a, b, and c are constants which are not subject to random
variation
and assuming that the errors in X1 and X2 are not correlated with each
other.

I got the impression that Jerry's question was homework and
that he would benefit from the exercise. After all, this
is sci.stat.math and not sci.stat.consult (Well, OK, it is not
sci.stat.edu either).

Well, he did it correctly and, hopefully, learned from it. If he had
done it wrong I would have pointed out his mistake and given
him the correct answer.

If I thought that Jerry was a working man and needed the
answer quickly to continue an expensive project I would
have stated the answer followed by a concise proof of
a couple of lines.

I assume, from Jerry's response, that I guessed correctly.

Sorry for irritating you, but you knew the answer. Right?

Greg

Greg Heath wrote:
Jerry wrote:
hi, here is the question,

if we know,
y = a * X1 + b * X2 + c

and we also know the variance of X1 and X2, how to evaluate the
variance of the Y?

Plug in and simplify:

VAR(y) = E{ (y - E{y} )^2 }

Hope this helps.

Greg

.

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