[R] A basic statistics question

Ron Michael ron_michael70 at yahoo.com
Tue Aug 12 21:57:29 CEST 2014


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.

Data <- structure(c(7L, 5L, 9L, 7L, 8L, 7L, 6L, 6L, 5L, 7L, 8L, 6L, 7L,  7L, 6L, 7L, 7L, 6L, 8L, 6L, 7L, 7L, 7L, 8L, 7L, 9L, 8L, 7L, 7L,  0L, 10L, 10L, 10L, 7L, 6L, 8L, 5L, 5L, 6L, 6L, 7L, 11L, 9L, 10L,  0L, 13L, 13L, 10L, 7L, 7L, 7L, 10L, 7L, 5L, 8L, 7L, 10L, 10L,  10L, 6L, 7L, 6L, 6L, 8L, 8L, 7L, 7L, 7L, 7L, 8L, 7L, 8L, 6L,  6L, 8L, 7L, 4L, 7L, 7L, 10L, 10L, 6L, 7L, 7L, 12L, 12L, 8L, 5L,  5L, 5L, 5L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 5L, 4L, 5L, 5L, 5L, 6L,  7L, 5L, 7L, 5L, 7L, 7L, 7L, 7L, 8L, 7L, 6L, 7L, 7L, 6L, 7L, 7L,  6L, 4L, 4L, 6L, 6L, 7L, 8L, 7L, 11L, 10L, 8L, 7L, 6L, 6L, 11L,  5L, 4L, 6L, 6L, 6L, 7L, 8L, 7L, 12L, 4L, 4L, 2L, 5L, 6L, 7L,  6L, 6L, 5L, 6L, 5L, 7L, 7L, 7L, 6L, 5L, 6L, 6L, 5L, 5L, 6L, 6L,  4L, 4L, 5L, 10L, 10L, 7L, 7L, 6L, 4L, 6L, 10L, 7L, 4L, 6L, 6L,  6L, 8L, 8L, 8L, 7L, 8L, 9L, 10L, 7L, 6L, 6L, 8L, 6L, 8L, 3L,  3L, 4L, 5L, 5L, 6L, 5L, 5L, 6L, 4L, 8L, 7L, 3L, 5L, 6L, 9L, 8L,  9L, 10L, 8L, 9L, 8L, 9L, 8L, 8L, 9L, 11L, 10L, 9L, 9L, 13L,
 13L,  10L, 7L, 7L, 7L, 9L, 8L, 7L, 6L, 10L, 8L, 7L, 8L, 8L, 3L, 4L,  3L, 7L, 6L, 6L, 6L, 6L, 5L, 6L, 6L, 6L, 2L, 5L, 7L, 9L, 8L, 9L,  10L, 8L, 8L, 9L, 9L, 11L, 11L, 11L, 10L, 9L, 9L, 11L, 2L, 3L,  2L, 2L, 2L, 1L, 4L, 4L, 2L, 2L, 1L, 1L, 1L, 3L, 3L, 4L, 6L, 4L,  5L, 2L, 3L, 5L, 4L, 4L, 2L, 4L, 4L, 5L, 4L, 2L, 7L, 3L, 3L, 10L,  13L, 11L, 9L, 9L, 7L, 8L, 9L, 6L, 7L, 6L, 5L, 3L, 13L, 3L, 3L,  0L, 1L, 4L, 5L, 3L, 3L, 0L, 2L, 20L, 3L, 2L, 6L, 5L, 5L, 5L,  2L, 2L, 5L, 5L, 5L, 4L, 3L, 4L, 4L, 3L, 4L, 10L, 10L, 9L, 8L,  4L, 4L, 8L, 7L, 10L, 3L, 1L, 9L, 5L, 11L, 9L), .Dim = c(45L,  8L), .Dimnames = list(NULL, c("V1", "V7", "V13", "V19", "V25",  "V31", "V37", "V43"))) 

Data_Normalized <- apply(Data, 2, function(x) return((x - mean(x))/sd(x))) 

(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?

Thanks for your pointer. 

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