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 <cbe...@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 >> >> -- >> 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@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 > Dept of Family/Preventive > Medicine > E mailto:cbe...@tajo.ucsd.edu UC San Diego > http://famprevmed.ucsd.edu/faculty/cberry/ 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@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.
