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.
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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