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

[chen jia]

OK. Thanks again.

I will read the references more.

Best,
Jia

On Thu, Jul 8, 2010 at 10:51 AM,  <markleeds at verizon.net> wrote:
> 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
>>>
>>> --
>>>                        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.
>>>
>>
>> Charles C. Berry                            (858) 534-2098
>>                                            Dept of Family/Preventive
>> Medicine
>> E mailto:cberry at 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 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.
>



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