R help - Mar 2012 - How to test the statistical significance of the difference of two univariate Linear Regression betas?

How to test the statistical significance of the difference of two
univariate Linear Regression betas?

Hi all,

There are two samples of data: D1 and D2.

On data D1 we do a univariate Linear Regression and get the coefficient
beta1.

On data D2 we do a univariate Linear Regression and get the coefficient
beta2.

How do I test the statistical significance of (beta1-beta2)?

Could you please recommend packages/commands in R for doing this?

Thanks a lot!

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Hi: I'm jot sure if it's exactly what you want but check out
Hotelling's
paper from 1940. It
should be in the archives because I answered this question before ( not
from you ).
If you can't find it, I'll find the title .... actually, here's the
title:

Hotelling, The Selection of Variates For Use in Prediction with Some
Comments on the
General Problem of Nuisance Parameters", Annals of Mathematical Statistics,
11,
271-283.




On Wed, Mar 14, 2012 at 11:21 AM, Michael <comtech.usa@gmail.com> wrote:
> How to test the statistical significance of the difference of two
> univariate Linear Regression betas?
>
> Hi all,
>
> There are two samples of data: D1 and D2.
>
> On data D1 we do a univariate Linear Regression and get the coefficient
> beta1.
>
> On data D2 we do a univariate Linear Regression and get the coefficient
> beta2.
>
> How do I test the statistical significance of (beta1-beta2)?
>
> Could you please recommend packages/commands in R for doing this?
>
> Thanks a lot!
>
>        [[alternative HTML version deleted]]
>
> ______________________________________________
> 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.
>
	[[alternative HTML version deleted]]

On Mar 14, 2012, at 16:21 , Michael wrote:
> How to test the statistical significance of the difference of two
> univariate Linear Regression betas?
> 
> Hi all,
> 
> There are two samples of data: D1 and D2.
> 
> On data D1 we do a univariate Linear Regression and get the coefficient
> beta1.
> 
> On data D2 we do a univariate Linear Regression and get the coefficient
> beta2.
> 
> How do I test the statistical significance of (beta1-beta2)?
> 
> Could you please recommend packages/commands in R for doing this?
Well, the large-sample test would be to calculate the se of the difference as 

  se <- sqrt(se1^2+se2^2)

and then Z <- (beta1-beta2)/se; 2*pnorm(-abs(Z)).

For small samples you might consider joining the two data sets and test for an
interaction between your predictor and an indicator for D1 or D2. Other options
are possible, if you know a bit of theory.
> 
> Thanks a lot!
> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
> 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.
-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com