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

[markleeds at verizon.net]

   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. Â 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:
     >
     > Â  Â  Â  Â 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. Â 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
     >>
     >> --
     >> Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â Ohio State University - Finance
     >> Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â 248 Fisher Hall
     >> Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  2100 Neil Ave.
     >>                             Columbus, Ohio  43210
     >> Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â Telephone: 614-292-2830
     >> Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â http://www.fisher.osu.edu/~chen_1002/
     >>
     >> ______________________________________________
     >> R-help at r-project.org mailing list
     >> https://stat.ethz.ch/mailman/listinfo/r-help
     >> PLEASE do read the posting guide
     >> http://www.R-project.org/posting-guide.html
     >> and provide commented, minimal, self-contained, reproducible code.
     >>
     >
     > Charles C. Berry                            (858) 534-2098
     > Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â  Â Dept of
     Family/Preventive
     > Medicine
     > E mailto:cberry at tajo.ucsd.edu               UC San Diego
     >  http://famprevmed.ucsd.edu/faculty/cberry/ Â La Jolla, San Diego
     92093-0901
     >
     >
     >
     --
     Ohio State University - Finance
     248 Fisher Hall
     2100 Neil Ave.
     Columbus, Ohio 43210
     Telephone: 614-292-2830
     http://www.fisher.osu.edu/~chen_1002/
     ______________________________________________
     R-help at r-project.org mailing list
     https://stat.ethz.ch/mailman/listinfo/r-help
     PLEASE do read the posting guide
     http://www.R-project.org/posting-guide.html
     and provide commented, minimal, self-contained, reproducible code.