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
--
Ohio State University - Finance
248 Fisher Hall
2100 Neil Ave.
Columbus, Ohio 43210
Telephone: 614-292-2830
http://www.fisher.osu.edu/~chen_1002/
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