# [R] R: generating independent vectors

From: Clark Allan <Allan_at_STATS.uct.ac.za>
Date: Fri 11 Mar 2005 - 23:47:02 EST

i would like to generate independent vectors. i have included the code below. i display the correlation matrix of the n*p (n=the number of samples, p= the number of variables) matrix. what i find is that as n increases, the correlation matrix tends to an identity matrix. i.e. independence. for small samples (see examples below, for n=20, p=5 ; n=50,p=5, n=100,p=5; n=10000,p=5) the variables does not appear to be independent. note that i have not tested this statement statistically.

ARE these variables independent? by setting the seed for each variable run i HOPE that the variables are now independent. IS this true??? if not does anyone know how to generate these independent variables?

how does R generate its random variables? does it use the box muller technique? if so how does it generate the random uniform variables?

***
allan

IND<-function(rows.=10,col.=3)
{
a<-matrix(nrow=rows.,ncol=col.)
for (j in 1:col.)
{

```	set.seed(j)
r<-rnorm(rows.)
a[,j]<-r
```

}
#list(a=a,cor=cor(a))
cor(a)
}
IND(rows.=10,col.=3)

> IND(rows.=20,col.=5)

[,1] [,2] [,3] [,4] [,5]
[1,] 1.00000000 0.25677165 -0.14882130 -0.09190797 0.1562481
[2,] 0.25677165 1.00000000 0.02585515 0.13735712 -0.1443301
[3,] -0.14882130 0.02585515 1.00000000 -0.11311416 0.1437001
[4,] -0.09190797 0.13735712 -0.11311416 1.00000000 0.1833647
[5,] 0.15624807 -0.14433011 0.14370006 0.18336467 1.0000000

> IND(rows.=50,col.=5)

[,1] [,2] [,3] [,4] [,5]
[1,] 1.0000000000 0.07915025 0.0009239851 -0.14102117 -0.07335342
[2,] 0.0791502463 1.00000000 -0.1764530631 0.10021081 0.19742285
[3,] 0.0009239851 -0.17645306 1.0000000000 0.02968062 0.14543350
[4,] -0.1410211698 0.10021081 0.0296806188 1.00000000 0.07234953
[5,] -0.0733534183 0.19742285 0.1454335014 0.07234953 1.00000000
>

> IND(rows.=100,col.=5)

[,1] [,2] [,3] [,4] [,5]
[1,] 1.00000000 -0.1537208 -0.023741715 -0.135245915 0.01961224
[2,] -0.15372076 1.0000000 -0.141796984 0.157219334 0.15518443
[3,] -0.02374171 -0.1417970 1.000000000 0.005865698 0.19118563
[4,] -0.13524592 0.1572193 0.005865698 1.000000000 0.07345299
[5,] 0.01961224 0.1551844 0.191185627 0.073452993 1.00000000
>

> IND(rows.=10000,col.=5)

[,1] [,2] [,3] [,4] [,5]
[1,] 1.000000000 0.015928444 -0.008288940 -0.005646904 0.006936662
[2,] 0.015928444 1.000000000 -0.005444611 0.005242395 -0.008246009
[3,] -0.008288940 -0.005444611 1.000000000 0.007277489 0.012299247
[4,] -0.005646904 0.005242395 0.007277489 1.000000000 0.001918704
[5,] 0.006936662 -0.008246009 0.012299247 0.001918704 1.000000000

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