R help - Aug 2004 - after lm-fit: equality of two regression coefficients test

Hi

Let's assume, we have a multiple linear regression, such as the one 
using the Scottish hills data (MASS, data(hills)):

one dependent variable: time
two independent var (metric): dist, climb

if I am interested, after (!) fitting a lm:

	my. lm <- lm(time ~ dist + climb, data = hills)

in the equivalence (or non-equivalence) of the two predictors "dist"
and
"climb":

	H0: dist = climb

Is there any function in R, which lets me calculate this, in just giving 
the lm-object "my.lm" and e.g. a vector such as c(1, -1), 
operationalizing the hypothesis H0: t(c(1, -1)) %*% c(dist, climb) = 0 ?

many thanks

Cheers!

Christoph

On Mon, 30 Aug 2004, Christoph Lehmann wrote:
> Hi
> 
> Let's assume, we have a multiple linear regression, such as the one 
> using the Scottish hills data (MASS, data(hills)):
> 
> one dependent variable: time
> two independent var (metric): dist, climb
> 
> if I am interested, after (!) fitting a lm:
> 
> 	my. lm <- lm(time ~ dist + climb, data = hills)
> 
> in the equivalence (or non-equivalence) of the two predictors
"dist" and
> "climb":
> 
> 	H0: dist = climb
I think you intend to ask if the *coefficients* in the fit should be 
equal, which is nonsense in this example of course.
> Is there any function in R, which lets me calculate this, in just giving 
> the lm-object "my.lm" and e.g. a vector such as c(1, -1), 
> operationalizing the hypothesis H0: t(c(1, -1)) %*% c(dist, climb) = 0 ?
library(car)
?linear.hypothesis


-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

Hi Christoph,
If you are interested in testing for b1=b2 in a regression model, say

y=b0+b1*x1+b2*x2+e

you can compare the two models o1 and o2

o1<-lm(y~x1+x2)
o2<-lm(y~I(x1+x2))

best,
vito


----- Original Message -----
From: Christoph Lehmann <christoph.lehmann at gmx.ch>
To: <R-help at stat.math.ethz.ch>
Sent: Monday, August 30, 2004 12:14 PM
Subject: [R] after lm-fit: equality of two regression coefficients test

> Hi
>
> Let's assume, we have a multiple linear regression, such as the one
> using the Scottish hills data (MASS, data(hills)):
>
> one dependent variable: time
> two independent var (metric): dist, climb
>
> if I am interested, after (!) fitting a lm:
>
> my. lm <- lm(time ~ dist + climb, data = hills)
>
> in the equivalence (or non-equivalence) of the two predictors
"dist" and
> "climb":
>
> H0: dist = climb
>
> Is there any function in R, which lets me calculate this, in just giving
> the lm-object "my.lm" and e.g. a vector such as c(1, -1),
> operationalizing the hypothesis H0: t(c(1, -1)) %*% c(dist, climb) = 0 ?
>
> many thanks
>
> Cheers!
>
> Christoph
>
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