[R] Principal Components Loadings

[Pavneet Arora]

Hello All,

I have a dataset "bodysize.Rdata" from Journal of Statistics Education 
Data Archive, which I have attached here.
I am trying to do principal components analysis on it using princomp, and 
it seems to be working fine. However, I am really struggling in 
interpretating the loadings of PCA, so I can answer questions like:

"What features of the body sizes do the first few components reflect?"

So for my R Analysis - following is what I have done:
body.pc <- princomp(bodysize,cor=T)
summary(body.pc)
body.pc$loadings
print(body.pc$loadings,cutoff=0.1,digits=1)


The book suggests that the answer to the above question should be:
it is easy to see that the first component reflects variations in overall 
size
of body; the second contrasts arm size (mostly) with body and leg size; 
the
third contrasts leg with rest of body, and the fourth is body against 
limbs. If
we plot PC1 against PC2 (i.e., scores on first component against those on 
the
second) with

plot(body.pc$scores[,2],body.pc$scores[,1])

we can see one outlier at the bottom of the plot and two to the left. 
Noting
the signs of the loadings on the first component (vertical axis), we can 
see that
the outlier at the bottom arises from a subject with large measurements. 
The
two outliers to the left are from people of average size but with 
proportionately
well-developed arms by comparison with their legs. Using identify() gives

identify(body.pc$scores[,2],body.pc$scores[,1])

which reveals that these outliers are observations 39 (lower) and 31 and 
86
(rightmost).


But I am really struggling to see how the first component reflect 
variations in overall size and the second in arm and so on forth. Please 
help?
Also when I try to use the "identify" function in R, all I get is "no 
point with 0.25m" or R crashes. How does one use the "identify" function 
in R?



Thanks in Advance





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***********************************************************************************************************************************************************************************************************************
MORE TH>N is a trading style of Royal & Sun Alliance Insurance plc (No. 93792). Registered in England and Wales at St. Mark’s Court, Chart Way, Horsham, West Sussex, RH12 1XL. 

Authorised by the Prudential Regulation Authority and regulated by the Financial Conduct Authority and the Prudential Regulation Authority.
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