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Re: st: RES: generating a variable with pre-specified correlations with other two (given) variables


From   Richard Williams <richardwilliams.ndu@gmail.com>
To   statalist@hsphsun2.harvard.edu, statalist@hsphsun2.harvard.edu
Subject   Re: st: RES: generating a variable with pre-specified correlations with other two (given) variables
Date   Wed, 31 Aug 2011 09:01:10 -0500

At 07:47 AM 8/31/2011, Tirthankar Chakravarty wrote:
Throw in some orthogonal, zero mean noise when constructing Z:

g z = .15625*x+.40625*y + runiform()

I believe that will zap the correlations though, won't it? i.e. the correlations of z with x and y will get smaller.

> P.D. The reason I want to run the aforementioned regression is the
> following. Suppose I have an initial regression of y on x, and x turns
> out to be insignificantly different from zero at some chosen
> confidence level. Then I want to generate an example in which adding a
> new (artificial) variable z as a covariate I can get x to become
> significantly different from zero at the same confidence level. Based
> on the formula for the t-test, I think I can do this if I can control
> the correlations between the artificial variable and the original
> ones. The excercise is just for expositional purposes, I do not want
> to attach any deep meaning to it.

If this is just for expositional purposes, it would probably be easier just to fake all the data with corr2data, rather than trying to create a combo of fake and real data. I think you could add a variable e that had 0 correlation with x and y and nonzero correlation with z. I generally find it is easier to get fake data to behave the way I want rather than real data.


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Richard Williams, Notre Dame Dept of Sociology
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