I was investigating the interpretation of a biplot and meaning of loadings/scores in PCA in this question: What are the principal components scores?

According to the author of the first answer the scores in his example are:

      x       y
John  -44.6  33.2
Mike  -51.9   48.8
Kate  -21.1   44.35

According to the second answer in Interpretation of biplots in principal components analysis in R,

The left and bottom axes are showing [normalized] principal component scores; the top and right axes are showing the loadings.

So, theoretically after plotting the biplot from "What are principal components scores" I should get on the left and bottom axes the scores as above and on the right and top the loadings.

I entered the data he provided in R:

DF<-data.frame(Maths=c(80, 90, 95), Science=c(85, 85, 80), English=c(60, 70, 40), Music=c(55, 45, 50))
pca = prcomp(DF, scale = FALSE)

This is the plot I got: Firstly, the left and bottom axis represent the loadings of the principal components. The top and right axis represent the scores BUT they do not correspond to the scores the author from the post provided (3 aka Kate has positive scores on the plot but one negative on PC1 according to the Tony Breyal in the first answer to the question in the post).

If I am doing or understanding something wrong, where is my mistake?

enter image description here

  • 1
    $\begingroup$ Let me offer you to read my answer which shows step by step computations of PCA. It might help you. $\endgroup$ – ttnphns May 14 '15 at 9:21
  • $\begingroup$ Hi Anni, I have just come across this question. Unfortunately, the scores provided under your first link are completely wrong. I commented there and hope this will get fixed. Apart from that, biplot shows you normalized scores; they are on the left and bottom. $\endgroup$ – amoeba Sep 23 '15 at 16:53

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