How do I test against a simple null that two regressions coefficients are equal?

hi: no. it's not the same. if you read the paper that I referenced last
night, that explains how to do the following? test :

Ho: R2 = R1

H1: R2 != R1

that's a different test from what you did but i think it's what you want.




On Jul 8, 2010, chen jia <chen_1002 at fisher.osu.edu> wrote:

Thanks, Chuck. I am reading the references, which are helpful.

Just to understand what I have done wrong here,

I proposed an alternative testing strategy:
I run regressions y = a3 + b1 * x + b2 * z + e3 and test alternative
hypothesis b1 != b2 against the null hypothesis b1 = b2 in this
equation.

Is it this the same test as

y = a1 + b1*x + e1
y = a2 + b2*x + e2
test alternative hypothesis b1 != b2 against null hypothesis b1 = b2.

Best,
Jia

On Wed, Jul 7, 2010 at 11:12 PM, Charles C. Berry <cberry at tajo.ucsd.edu>
wrote:

On Wed, 7 Jul 2010, chen jia wrote:

Hi there,

I run two regressions:

y = a1 + b1 * x + e1
y = a2 + b2 * z + e2

I want to test against the null hypothesis: b1 = b2. ?How do I design the
test?

You are testing a non-nested hypothesis, which requires special handling.

The classical test is due to Hotelling, but see the references (and R code
snippets) in this posting:

? ? ? ?http://markmail.org/message/egnowmdzpzjtahy7

(it is the merest coincidence that the above thread was initiated by Mark
Leeds and that the URL is 'markmail' :-) )

HTH,

Chuck

I think I can add two equations together and divide both sides by 2:
y = 0.5*(a1+a2) + 0.5*b1 * x + 0.5*b2 * z + e3, where e3 = 0.5*(e1 + e2).
or just y = a3 + 0.5*b1 * x + 0.5*b2 * z + e3

If I run this new regression, I can test against the null b1 = b2 in
this regression. ?Is it an equivalent test as the original one? If
yes, how do I do that in R?

Alternatively, I think I can just test against the null:
correlation(y, x) = correlation(y, z), where correlation(. , .) is the
correlation between two random variables. Is this equivalent too? If
yes, how do I do it in R?

Thanks.

Best,
Jia

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Charles C. Berry ? ? ? ? ? ? ? ? ? ? ? ? ? ?(858) 534-2098
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Medicine
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Ohio State University - Finance
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Columbus, Ohio 43210
Telephone: 614-292-2830
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