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From: dc353 on 22 Mar 2010 09:57
On Mar 22, 9:16 am, Paige Miller <paige.mil...(a)kodak.com> wrote:
> On Mar 19, 2:05 pm, "dc...(a)hotmail.com" <dc...(a)hotmail.com> wrote:
>
> > the population correlation may be 0 but the sample correlation isn't.
> > I'm looking to create a second random variable with sample correlation
> > of 0, once that's done getting the sample correlation to equal .2 is
> > relatively straightforward.
>
> Okay, so now you go from talking about random variables to samples.
> Different animal. You simply need to take your first vector of
> observations, and create a vector orthogonal to it. Simple geometry.
>
> > If you use the rand() function in excel
> > and create two random variables you quickly see what I'm talking
> > about.
>
> Since I never use the rand() function in Excel (and in fact, never use
> Excel for anything statistical), I do not "quickly see what you are
> talking about". Perhaps you could explain what you are talking about
> here without referring to Excel.
>
> --
> Paige Miller
> paige\dot\miller \at\ kodak\dot\com

Paige,

It's just the difference between a population statistic and a sample
statistic. Use any statistical package and create two random
variables with n observations. When you measure the correlation over
the sample it won't be 0. As n increases the correlation will get
closer and closer to 0. The distribution of sample correlations
should have a mean of 0 but any one of them will be different.
From: xlr82sas on 22 Mar 2010 20:08
On Mar 22, 6:57 am, "dc...(a)hotmail.com" <dc...(a)hotmail.com> wrote:
> On Mar 22, 9:16 am, Paige Miller <paige.mil...(a)kodak.com> wrote:
>
>
>
> > On Mar 19, 2:05 pm, "dc...(a)hotmail.com" <dc...(a)hotmail.com> wrote:
>
> > > the population correlation may be 0 but the sample correlation isn't.
> > > I'm looking to create a second random variable with sample correlation
> > > of 0, once that's done getting the sample correlation to equal .2 is
> > > relatively straightforward.
>
> > Okay, so now you go from talking about random variables to samples.
> > Different animal. You simply need to take your first vector of
> > observations, and create a vector orthogonal to it. Simple geometry.
>
> > > If you use the rand() function in excel
> > > and create two random variables you quickly see what I'm talking
> > > about.
>
> > Since I never use the rand() function in Excel (and in fact, never use
> > Excel for anything statistical), I do not "quickly see what you are
> > talking about". Perhaps you could explain what you are talking about
> > here without referring to Excel.
>
> > --
> > Paige Miller
> > paige\dot\miller \at\ kodak\dot\com
>
> Paige,
>
> It's just the difference between a population statistic and a sample
> statistic.  Use any statistical package and create two random
> variables with n observations.  When you measure the correlation over
> the sample it won't be 0.  As n increases the correlation will get
> closer and closer to 0.  The distribution of sample correlations
> should have a mean of 0 but any one of them will be different.

Hi,

Here is some code based on a previous post

It produces Y with a ~.5 correlation with X.

data p5;
seed1 = 373765061;
seed2 = 535327321;
r=0.50;
r2=r*r;
do i=1 to 1000000;
x = rannor(seed1);
y = rannor(seed2);
y = x*r + y*sqrt(1-r2);
keep x y;
output;
end;
run;

proc corr data=p5;
var x;
with y;
run;

Pearson Correlation Coefficients, N = 1000000
Prob > |r| under H0: Rho=0

X

Y 0.49864
<.0001
From: adjgiulio on 23 Mar 2010 15:42
Just thinking out loud. Say your known variable is X, with n
observations. Create a random variable Y for the first n-1
observations of X. Then calculate the n-th value of Y so that r is
whatever you want it to be. To do that, invert the r formula. r is a
function of x, y and their means. If you know all values but y(n),
then inverting the formula should be easy and you would end up with
the exact value of r you want.
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