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

 From Tirthankar Chakravarty <[email protected]> To [email protected] Subject Re: st: RES: generating a variable with pre-specified correlations with other two (given) variables Date Wed, 31 Aug 2011 06:18:39 -0700

```Yes, I meant -rnormal()-. Adding zero mean noise will, as Nick and
Richard note, inflate the variance of Z (and so affect the
correlations), but leave the covariances intact.

T

On Wed, Aug 31, 2011 at 6:14 AM, Nick Cox <[email protected]> wrote:
> Richard's question is the more crucial one, but I guess that
> average (although that could easily be fixed). Either way, adding
> noise will reduce the correlations.
>
> Nick
>
> On Wed, Aug 31, 2011 at 3:01 PM, Richard Williams
> <[email protected]> wrote:
>> 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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--
Tirthankar Chakravarty
[email protected]
[email protected]

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```

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