[R] A basic statistics question
Rolf Turner
r.turner at auckland.ac.nz
Tue Aug 12 23:41:52 CEST 2014
On 13/08/14 07:57, Ron Michael wrote:
> Hi,
>
> I would need to get a clarification on a quite fundamental statistics property, hope expeRts here would not mind if I post that here.
>
> I leant that variance-covariance matrix of the standardized data is equal to the correlation matrix for the unstandardized data. So I used following data.
<SNIP>
> (t(Data_Normalized) %*% Data_Normalized)/dim(Data_Normalized)[1]
>
>
>
> Point is that I am not getting exact CORR matrix. Can somebody point me what I am missing here?
You are using a denominator of "n" in calculating your "covariance"
matrix for your normalized data. But these data were normalized using
the sd() function which (correctly) uses a denominator of n-1 so as to
obtain an unbiased estimator of the population standard deviation.
If you calculated
(t(Data_Normalized) %*% Data_Normalized)/(dim(Data_Normalized)[1]-1)
then you would get the same result as you get from cor(Data) (to within
about 1e-15).
cheers,
Rolf Turner
--
Rolf Turner
Technical Editor ANZJS
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