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

[Charles C. Berry]

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
                                             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