[R] Principal Components Loadings

[David Carlson]

Look at the results of summary(body.pc). You will see that the
first component accounts for 70% of the variability. That is
very large and suggests that the variables are highly correlated
with one another. You could check with cor(bodysize). None of
the correlations is negative and the smallest one is .41905.
That is strong evidence that body size is the main contributor
to variation among the variables. Now look at the loadings for
the first principal component. These are all negative and about
the same magnitude. It is not the sign of the loadings, but the
fact that they are all the same sign that indicates the first
component measures size. The loadings provide the weights for
computing the principal component scores. If we multiply the
loadings by the standard deviation for each component, we get a
structure matrix (also sometimes called loadings) that
represents the correlation of each variable with the component:

sweep(body.pc$loadings, 2, body.pc$sdev, "*")

The absolute value of the correlations for the variables with
the first component are high with the lowest being .653, again
suggesting that the first component reflects size. If you look
at Component 2, the interpretation is not so straightforward.
Only ankle is moderately large (-.533) and forearm and wrist are
also negative but smaller. Chest, abdomen, hip, and thigh are
all positive. The component seems to be contrasting bigger trunk
development (positive direction) against limb development
(negative direction). 

You raised a question about using identify() but you also
reported using it successfully to identify outliers. The
commands you posted work fine for me to identify the outliers. 

-------------------------------------
David L Carlson
Department of Anthropology
Texas A&M University
College Station, TX 77840-4352

-----Original Message-----
From: r-help-bounces at r-project.org
[mailto:r-help-bounces at r-project.org] On Behalf Of Pavneet Arora
Sent: Wednesday, March 26, 2014 4:23 AM
To: John Kane
Cc: r-help at r-project.org
Subject: Re: [R] Principal Components Loadings

Hello John

As per your suggestion, I have now used the dput function. So my
Rdata 
dataset "bodysize" looks like this.

> dput(bodysize)
structure(list(neck = c(36.2, 38.5, 34, 37.4, 34.4, 39, 36.4, 
37.8, 38.1, 42.1, 38.5, 39.4, 38.4, 39.4, 40.5, 36.4, 38.9,
42.1, 
38, 40, 39.1, 41.3, 33.9, 35.5, 34.5, 35.7, 36.2, 38.8, 36.4, 
36.7, 38.7, 37.3, 38.1, 39.8, 42.1, 38.4, 38.5, 42.1, 51.2,
40.2, 
43.2, 36.6, 37.3, 41.5, 31.5, 35.7, 33.6, 34.6, 32.8, 34, 34.9, 
34.3, 36.5, 35.1, 37.8, 39.9, 39.1, 40.5, 40.5, 38.4, 41.4,
35.6, 
38, 37.4, 40.1, 40.9, 35.6, 36.9, 37.5, 36.3, 35.5, 38.7, 36.4, 
33.2, 36.5, 36, 38.7, 38.7, 37.8, 37.4, 38.4, 38.1, 39.3, 38.7, 
38.5, 36.5, 37.7, 36.5, 38, 36.7, 37.2, 39.2, 37.5, 38, 37.3, 
41.1, 37.5, 38.7, 35.9, 40, 40.1, 37, 36.3, 40.7, 39.6, 31.1, 
38.6, 42, 38.5, 34.2, 37.2, 37.1, 40.2, 35.3, 38, 36.3, 36.8, 
41, 38.3, 38, 40.8, 39.5, 36.9, 36.9, 37.7, 36.6, 38.9, 37.5, 
39.8, 38.3, 35.5, 36.3, 37.8, 37.8, 36.5, 37.8, 37, 37.7, 34.3, 
40.8, 37.4, 36.5, 37.5, 35.5, 38, 35.7, 39.2, 40.9, 35.2, 40.6, 
35.4, 41.8, 34.1, 37.9, 38.2, 35.6, 38.5, 37, 35.9, 36.2, 35, 
38.5, 40.7, 36, 39.5, 40.5, 38.5, 43.9, 40.4, 37.6, 37, 34,
38.4, 
38.7, 41.5, 36, 35.3, 42.1, 38, 42.8, 40, 33.8, 35.5, 35.3,
37.7, 
39.4, 41.9, 38.5, 40.8, 38, 36.4, 41.8, 40.7, 38.5, 35.4, 38.5, 
35.5, 36.5, 37.6, 37.4, 37.8, 35.2, 37.9, 37.9, 40.9, 41.9,
39.1, 
40.2, 36, 34.5, 35.8, 40.2, 38.3, 39, 37.4, 41.2, 34.8, 36.9, 
39.4, 37.6, 38.5, 42.5, 37.4, 35.2, 41.1, 33.4, 37.2, 38.3,
38.1, 
37.4, 35.2, 39.4, 38, 35.1, 40.4, 38.3, 40.6, 40.2, 37.9, 40.8, 
34.7, 38.8, 41.4, 41.3, 40.7, 36.3, 40.8, 34.9, 40.9, 38.9,
38.9, 
40.8), chest = c(93.1, 93.6, 95.8, 101.8, 97.3, 104.5, 105.1, 
99.6, 100.9, 99.6, 101.5, 103.6, 102, 104.1, 101.3, 99.1, 101.9,

107.6, 106.8, 106.2, 103.3, 111.4, 86, 86.7, 90.2, 89.6, 88.6, 
97.4, 93.5, 97.4, 100.5, 93.5, 93, 111.7, 117, 118.5, 106.5, 
105.6, 136.2, 114.8, 128.3, 106, 113.3, 106.6, 85.1, 96.6, 88.2,

89.8, 92.3, 83.4, 90.2, 89.2, 89.7, 93.3, 87.6, 107.6, 100,
111.5, 
115.4, 104.8, 112.3, 102.9, 107.6, 105.3, 105.3, 103, 90, 95.4, 
89.3, 94.4, 97.6, 88.5, 93.6, 87.7, 93.4, 91.6, 91.6, 102, 96.4,

102.7, 97.7, 97.1, 103.1, 101.8, 101.4, 98.9, 97.5, 104.3, 97.3,

96.7, 99.7, 101.9, 97.2, 106.6, 99.6, 113.2, 99.1, 99.4, 95.1, 
107.5, 106.5, 99.1, 96.7, 103.5, 104, 93.1, 105.2, 110, 110.1, 
97.8, 96.3, 108, 99.7, 93.5, 100.7, 97, 96, 99.2, 95.4, 101.8, 
104.3, 99.2, 99.3, 94, 98.9, 101, 98.7, 95.9, 103.9, 96.2, 97.8,

94.6, 103.6, 100.4, 98.4, 104.6, 92.9, 97.8, 98.3, 104.7, 98.6, 
99.5, 102.7, 92.1, 96.6, 92.7, 102, 110.9, 92.3, 114.1, 92.9, 
108.3, 88.5, 94, 101.1, 92.1, 105.6, 98.5, 88.7, 101.1, 94,
103.8, 
98.9, 89.2, 111.4, 107.5, 99.1, 108.2, 114.9, 99.1, 92.2, 90.8, 
100.5, 98.2, 115.3, 96.8, 92.6, 119.2, 102.7, 109.5, 108.5,
79.3, 
95.5, 92.3, 98.9, 89.5, 117.5, 107.4, 109.2, 103.4, 91.4, 115.2,

104.9, 106.7, 92.2, 101.6, 97.8, 92, 94, 103.7, 102.7, 91.1, 
107.2, 100.8, 121.6, 105.6, 100.6, 102.7, 99.8, 92.9, 91.2,
115.6, 
98.3, 103.7, 98.7, 119.8, 92.8, 93.3, 106.8, 93.9, 99, 119.9, 
94.2, 92.7, 106.9, 88.8, 101.7, 105.3, 104, 98.6, 99.6, 103.4, 
100.2, 94.9, 97.2, 104.7, 104, 117.6, 95.8, 106.4, 93, 119.6, 
119.7, 115.8, 118.3, 97.4, 113.7, 89.2, 108.5, 111.1, 108.3, 
112.4), abdomen = c(85.2, 83, 87.9, 86.4, 100, 94.4, 90.7, 88.5,

82.5, 88.6, 83.6, 90.9, 91.6, 101.8, 96.4, 92.8, 96.4, 97.5, 
89.6, 100.5, 95.9, 98.8, 76.4, 80, 76.3, 79.7, 74.6, 88.7, 73.9,

83.5, 88.7, 84.5, 79.1, 100.5, 115.6, 113.1, 100.9, 98.8, 148.1,

108.1, 126.2, 104.3, 111.2, 104.3, 76, 81.5, 73.7, 79.5, 83.4, 
70.4, 86.7, 77.9, 82, 79.6, 77.6, 100, 99.8, 104.2, 105.3, 98.3,

104.8, 94.7, 102.4, 99.7, 105.5, 100.3, 83.9, 86.6, 78.4, 84.6, 
91.5, 82.8, 82.9, 76, 83.3, 81.8, 78.8, 95, 95.4, 98.6, 95.8, 
89, 97.8, 94.9, 99.8, 89.7, 88.1, 90.9, 86, 86.5, 95.6, 93.2, 
83.1, 97.5, 88.8, 99.2, 91.6, 86.7, 88.2, 94, 95, 92, 89.2,
95.5, 
98.6, 87.3, 102.8, 101.6, 88.7, 92.3, 90.6, 105, 95, 89.6, 92.4,

86.6, 90, 90, 92.4, 87.5, 99.2, 98.1, 83.3, 86.1, 84.1, 89.9, 
92.1, 78, 93.5, 87, 90.1, 90.3, 99.8, 89.4, 87.2, 101.1, 86.1, 
98.6, 88.5, 106.6, 93.1, 93, 91, 77.1, 85.3, 81.9, 99.1, 100.5, 
76.5, 106.8, 77.6, 102.9, 72.8, 88.2, 100.1, 83.5, 105, 90.8, 
76.6, 92.4, 81.2, 95.6, 92.1, 83.4, 106, 95.1, 90.4, 100.4,
115.9, 
90.8, 81.9, 75, 90.3, 90.3, 108.8, 79.4, 83.2, 110.3, 92.7,
104.5, 
104.6, 69.4, 83.6, 86.8, 90.4, 83.7, 109.3, 98.9, 98, 101.2, 
80.6, 113.7, 94.1, 105.7, 85.6, 96.6, 86, 89.7, 78, 89.7, 89.2, 
85.7, 103.1, 89.1, 113.9, 96.3, 93.9, 101.3, 83.9, 84.4, 79.4, 
104, 89.7, 97.6, 87.6, 122.1, 81.1, 81.5, 100, 88.7, 91.8,
110.4, 
87.6, 82.8, 95.3, 78.2, 91.1, 96.7, 89.4, 93, 86.4, 96.7, 88.1, 
94.9, 93.3, 95.6, 98.2, 113.8, 82.8, 100.5, 79.7, 118, 109,
113.4, 
106.1, 84.3, 107.6, 83.6, 105, 111.5, 101.3, 108.5), hip =
c(94.5, 
98.7, 99.2, 101.2, 101.9, 107.8, 100.3, 97.1, 99.9, 104.1, 98.2,

107.7, 103.9, 108.6, 100.1, 99.2, 105.2, 107, 102.4, 109, 104.9,

104.8, 94.6, 93.4, 95.8, 96.5, 85.3, 94.7, 88.5, 98.7, 99.8, 
100.6, 94.5, 108.3, 116.1, 113.8, 106.2, 104.8, 147.7, 102.5, 
125.6, 115.5, 114.1, 106, 88.2, 97.2, 88.5, 92.7, 90.4, 87.2, 
98.3, 91, 89.1, 91.6, 88.6, 99.6, 102.5, 105.8, 97, 99.6, 103.1,

100.8, 99.4, 99.7, 108.3, 104.2, 93.9, 91.8, 96.1, 94.3, 98.5, 
95.5, 96.3, 88.6, 93, 94.8, 94.3, 98.3, 99.3, 100.2, 97.1, 96.9,

99.6, 95, 96.2, 96.2, 96.9, 93.8, 99.3, 98.3, 102.2, 100.6,
95.4, 
100.6, 101.4, 107.5, 102.4, 96.2, 92.8, 103.7, 101.7, 98.3,
98.3, 
101.6, 99.5, 96.6, 103.6, 100.7, 102.1, 100.6, 99.3, 103, 98.6, 
99.8, 97.5, 92.6, 99.7, 96.4, 104.3, 101, 104.1, 101.4, 97.5, 
95.2, 94, 100, 98.5, 93.2, 99.5, 97.8, 95.8, 99.1, 103.2, 92.3, 
98.4, 102.1, 95.6, 100.6, 98.3, 107.7, 101.6, 99.3, 98.9, 93.9, 
102.5, 95.3, 110.1, 106.2, 92.1, 113.9, 93.5, 114.4, 91.1, 95.2,

105, 98.3, 106.4, 102.5, 89.8, 99.3, 91.5, 105.1, 103.5, 89.6, 
108.8, 104.5, 95.6, 106.8, 111.9, 98.1, 92.8, 89.2, 98.7, 99.9, 
114.4, 89.2, 96.4, 113.9, 101.9, 109.9, 109.8, 85, 91.6, 96.1, 
95.5, 98.1, 108.8, 104.1, 101.8, 103.1, 92.3, 112.4, 102.7,
111.8, 
96.5, 100.6, 96.2, 101, 99, 94.2, 99.2, 96.9, 105.5, 102.6,
107.1, 
102, 100.1, 101.7, 91.8, 94, 89, 109, 99.1, 104.2, 96.1, 112.8, 
96.3, 94.4, 105, 94.5, 96.2, 105.5, 95.6, 91.9, 98.2, 87.5,
97.1, 
106.6, 98.4, 97, 90.1, 100.7, 97.8, 100.2, 94, 93.7, 101.1,
111.8, 
94.5, 100.5, 87.6, 114.3, 109.1, 109.8, 101.6, 94.4, 110, 88.8, 
104.5, 101.7, 97.8, 107.1), thigh = c(59, 58.7, 59.6, 60.1,
63.2, 
66, 58.4, 60, 62.9, 63.1, 59.7, 66.2, 63.4, 66, 69, 63.1, 64.8, 
66.9, 64.2, 65.8, 63.5, 63.4, 57.4, 54.9, 58.4, 55, 51.7, 57.5, 
50.1, 58.9, 57.5, 58.5, 57.3, 67.1, 71.2, 61.9, 63.5, 66, 87.3, 
61.3, 72.5, 70.6, 67.7, 65, 50, 58.4, 53.3, 52.7, 52, 50.6,
52.6, 
51.4, 49.3, 52.6, 51.9, 57.2, 62.1, 61.8, 59.1, 60.6, 61.6,
60.9, 
61, 60.8, 65, 64.8, 55, 54.3, 56, 51.2, 56.6, 58.9, 52.9, 50.9, 
55.5, 54.5, 56.7, 55, 53.5, 56.5, 54.8, 54.8, 58.9, 56, 56.3, 
54.7, 57.2, 57.8, 61, 60.4, 58.3, 58.9, 56.9, 58.9, 57.4, 61.7, 
60.6, 62.1, 54.7, 62.7, 59, 59.3, 60, 59.1, 59.5, 54.7, 61.2, 
55.8, 57.5, 57.5, 61.9, 63.7, 62.3, 61.5, 59.3, 55.9, 58.8,
56.8, 
64.6, 58.5, 58.5, 57.1, 60.5, 58.1, 58.5, 60.7, 60.7, 53.5,
61.7, 
57.4, 57, 60.3, 61.2, 56.1, 56, 58.9, 58.8, 63.6, 58.1, 66.5, 
59.1, 60.4, 57.1, 56.1, 59.1, 56.4, 71.2, 68.4, 51.9, 67.6,
56.9, 
72.9, 53.6, 56.8, 62.1, 57.3, 68.6, 60.8, 50.1, 59.4, 52.5,
61.4, 
64, 52.4, 63.8, 64.8, 55.5, 63.3, 74.4, 60.1, 54.7, 50, 57.8, 
59.2, 69.2, 50.3, 60, 69.8, 64.7, 69.5, 68.1, 47.2, 54.1, 58, 
55.4, 57.3, 67.7, 63.5, 62.8, 61.5, 54.3, 68.5, 60.6, 65.3,
60.2, 
61.1, 57.7, 62.3, 57.5, 58.5, 60.2, 55.5, 68.8, 60.6, 63.5,
63.3, 
58.9, 60.7, 53, 56, 51.1, 63.7, 56.3, 60, 57.1, 62.5, 53.8,
54.7, 
63.9, 53.7, 57.7, 64.2, 59.7, 54.4, 57.4, 50.8, 56.6, 64, 58.4, 
55.4, 53, 59.3, 57.1, 56.8, 54.3, 54.4, 59.3, 63.4, 61.2, 59.2, 
50.7, 61.3, 63.7, 65.6, 58.2, 54.3, 63.3, 49.6, 59.6, 60.3, 56, 
59.3), knee = c(37.3, 37.3, 38.9, 37.3, 42.2, 42, 38.3, 39.4, 
38.3, 41.7, 39.7, 39.2, 38.3, 41.5, 39, 38.7, 40.8, 40, 38.7, 
40.6, 38, 40.6, 35.3, 36.2, 35.5, 36.7, 34.7, 36, 34.5, 35.3, 
38.7, 38.8, 36.2, 44.2, 43.3, 38.3, 39.9, 41.5, 49.1, 41.1,
39.6, 
42.5, 40.9, 40.2, 34.7, 38.2, 34.5, 37.5, 35.8, 34.4, 37.2,
34.9, 
33.7, 37.6, 34.9, 38, 39.6, 39.8, 38, 37.7, 40.9, 38, 39.4,
40.1, 
41.2, 40.2, 36.1, 35.4, 37.4, 37.4, 38.6, 37.6, 37.5, 35.4,
35.2, 
37, 39.7, 38.3, 37.5, 39.3, 38.2, 38, 39, 36.5, 36.6, 37.8,
37.7, 
39.5, 38.4, 39.9, 38.2, 39.7, 38.3, 40.5, 39.6, 42.3, 39.4,
39.3, 
37.3, 39, 39.4, 38.4, 38.4, 39.8, 36.1, 39, 39.3, 38.7, 40,
36.8, 
38, 40, 38.1, 37.8, 38.1, 36.3, 38.4, 38.8, 41.1, 39.2, 39.3, 
40.5, 38.7, 36.5, 36.6, 36, 36.8, 35.8, 39, 36.9, 38.7, 38.5, 
38.1, 35.6, 36.9, 37.9, 36.1, 39.2, 38.4, 42.5, 39.6, 38.2,
36.7, 
36.1, 37.6, 36.5, 43.5, 40.8, 35.7, 42.7, 35.9, 43.5, 36.8,
37.4, 
40, 37.8, 40, 38.5, 34.8, 39, 36.6, 40.6, 37.3, 35.6, 42, 41.3, 
34.2, 41.7, 40.6, 39.1, 36.2, 34.8, 37.3, 37.7, 42.4, 34.8,
38.1, 
42.6, 39.5, 43.1, 42.8, 33.5, 36.2, 39.4, 38.9, 39.7, 41.3,
39.8, 
41.3, 40.4, 36.3, 45, 38.6, 43.3, 38.9, 38.4, 38.6, 38, 40, 39, 
39.2, 35.7, 38.3, 39, 40.3, 39.8, 37.6, 39.4, 36.2, 38.2, 35, 
40.3, 38.8, 40.9, 38.1, 36.9, 36.5, 39, 39.2, 36.2, 38.1, 42.7, 
40.2, 35.2, 37.1, 33, 38.5, 42.6, 37.4, 38.8, 35, 38.6, 38.9, 
35.9, 35.7, 37.1, 40.3, 41.1, 39.1, 38.1, 33.4, 42.1, 42.4, 46, 
38.8, 37.5, 44, 34.8, 40.8, 37.3, 41.6, 42.2), ankle = c(21.9, 
23.4, 24, 22.8, 24, 25.6, 22.9, 23.2, 23.8, 25, 25.2, 25.9,
21.5, 
23.7, 23.1, 21.7, 23.1, 24.4, 22.9, 24, 22.1, 24.6, 22.2, 22.1, 
22.9, 22.5, 21.4, 21, 21.3, 22.6, 33.9, 21.5, 24.5, 25.2, 26.3, 
21.9, 22.6, 24.7, 29.6, 24.7, 26.6, 23.7, 25, 23, 21, 23.4,
22.5, 
21.9, 20.6, 21.9, 22.4, 21, 21.4, 22.6, 22.5, 22, 22.5, 22.7, 
22.5, 22.9, 23.1, 22.1, 23.6, 22.7, 24.7, 22.7, 21.7, 21.5,
22.4, 
21.6, 22.4, 21.6, 23.1, 19.1, 20.9, 21.4, 24.2, 21.8, 21.5,
22.7, 
23.7, 22, 23, 24.1, 22, 33.7, 21.8, 23.3, 23.8, 24.4, 22.5,
23.1, 
22.1, 24.5, 24.6, 23.2, 22.9, 23.3, 21.9, 22.3, 22.3, 22.4,
23.2, 
25.4, 22, 24.8, 23.5, 23.4, 24.8, 22.8, 22.3, 23.6, 23.9, 21.9, 
21.8, 22.1, 22.8, 23.3, 24.8, 24.5, 24.6, 23.2, 22.6, 22.1,
23.5, 
21.9, 22.2, 20.8, 21.8, 22.2, 23.2, 23, 22.6, 20.5, 23, 22.7, 
22.4, 23.8, 22.5, 24.5, 21.6, 22, 22.3, 22.7, 23.2, 22, 25.2, 
24.6, 22, 24.7, 20.4, 25.1, 23.8, 22.8, 24.9, 21.7, 25.2, 25, 
21.8, 24.6, 21, 25, 23.5, 20.4, 23.4, 25.6, 21.9, 24.6, 24,
23.4, 
22.1, 22, 22.4, 21.5, 24, 22.2, 22, 24.8, 24.7, 25.8, 24.1,
20.2, 
21.8, 22.7, 22.4, 22.6, 24.7, 23.5, 24.8, 22.9, 21.8, 25.5,
24.7, 
26, 22.4, 24.1, 24, 22.3, 22.5, 24.1, 23.8, 22, 23.7, 24, 21.8, 
24.1, 21.4, 23.3, 22.5, 22.6, 21.7, 23.2, 23, 25.5, 21.8, 23.6, 
21.5, 22.6, 22.9, 22, 23.9, 27, 23.4, 22.5, 21.8, 19.7, 22.6, 
23.4, 22.5, 23.2, 21.3, 22.8, 23.6, 21, 21, 22.7, 23, 22.3,
22.3, 
24, 20.1, 23.4, 24.6, 25.4, 24.1, 22.6, 22.6, 21.5, 23.2, 21.5, 
22.7, 24.6), biceps = c(32, 30.5, 28.8, 32.4, 32.2, 35.7, 31.9, 
30.5, 35.9, 35.6, 32.8, 37.2, 32.5, 36.9, 36.1, 31.1, 36.2,
38.2, 
37.2, 37.1, 32.5, 33, 27.9, 29.8, 31.1, 29.9, 28.7, 29.2, 30.5, 
30.1, 32.5, 30.1, 29, 37.5, 37.3, 32, 35.1, 33.2, 45, 34.1,
36.4, 
33.6, 36.7, 35.8, 26.1, 29.7, 27.9, 28.8, 28.8, 26.8, 26, 26.7, 
29.6, 38.5, 27.7, 35.9, 33.1, 37.7, 31.6, 34.5, 36.2, 32.5,
32.7, 
33.6, 35.3, 34.8, 29.6, 32.8, 32.6, 27.3, 31.5, 30.3, 29.7,
29.3, 
29.4, 29.3, 30.2, 30.8, 31.4, 30.3, 29.4, 29.9, 34.3, 31.2,
29.7, 
32.4, 32.6, 29.2, 30.2, 28.8, 29.1, 31.4, 30.1, 33.3, 30.3,
32.9, 
31.6, 30.6, 31.6, 35.3, 32.2, 27.9, 31, 31, 30.1, 31, 30.5,
35.1, 
35.1, 32.1, 33.3, 33.5, 35.3, 30.7, 31.8, 29.8, 29.9, 33.4,
33.6, 
32.1, 33.9, 33, 34.4, 30.6, 34.4, 35.6, 33.8, 33.9, 33.3, 31.6, 
27.5, 31.2, 33.5, 33.6, 34, 30.9, 32.7, 34.3, 31.7, 35.5, 30.8, 
32, 31.6, 30.5, 31.8, 33.5, 36.1, 33.3, 25.8, 36, 31.6, 38.5, 
27.8, 30.6, 33.7, 32.2, 35.2, 31.6, 27, 30.1, 27, 31.3, 33.5, 
28.3, 34, 36.4, 30.2, 37.2, 36.1, 32.5, 30.4, 24.8, 31, 32.4, 
35.4, 31, 31.5, 34.4, 34.8, 39.1, 35.6, 27.7, 31.4, 30, 30.5, 
32.9, 37.2, 36.4, 36.6, 33.4, 29.6, 37.1, 34, 33.7, 31.7, 32.9, 
31.2, 30.8, 30.6, 33.8, 31.7, 29.4, 32.1, 32.9, 34.8, 37.3,
33.1, 
36.7, 31.4, 29, 30.9, 36.8, 29.5, 32.7, 28.6, 34.7, 31.3, 27.5, 
35.7, 28.5, 31.4, 38.4, 27.9, 29.4, 34.1, 25.3, 33.4, 33.2,
34.6, 
32.4, 31.7, 31.8, 30.9, 27.8, 31.3, 30.3, 32.6, 35.1, 29.8,
35.9, 
28.5, 34.9, 35.6, 35.3, 32.1, 29.2, 37.5, 25.6, 35.2, 31.3,
30.5, 
33.7), forearm = c(27.4, 28.9, 25.2, 29.4, 27.7, 30.6, 27.8, 
29, 31.1, 30, 29.4, 30.2, 28.6, 31.6, 30.5, 26.4, 30.8, 31.6, 
30.5, 30.1, 30.3, 32.8, 25.9, 26.7, 28, 28.2, 27, 26.6, 27.9, 
26.7, 27.7, 26.4, 30, 31.5, 31.7, 29.8, 30.6, 30.5, 29, 31,
32.7, 
28.7, 29.8, 31.5, 23.1, 27.4, 26.2, 26.8, 25.5, 25.8, 25.8,
26.1, 
26, 27.4, 27.5, 30.2, 28.3, 30.9, 28.8, 29.6, 31.8, 29.8, 29.9, 
29, 31.1, 30.1, 27.4, 27.4, 28.1, 27.1, 27.3, 27.3, 27.3, 25.7, 
27, 27, 29.2, 25.7, 26.8, 28.7, 27.2, 25.2, 29.6, 27.3, 26.3, 
27.7, 28, 28.4, 29.3, 29.6, 27.7, 28.4, 28.2, 29.6, 27.9, 30.8, 
30.1, 27.8, 27.5, 30.9, 31, 26.2, 29.2, 30.3, 27.2, 29.4, 28.5, 
29.6, 30.7, 26, 28.2, 27.8, 31.1, 27.6, 27.3, 26.3, 28, 29.8, 
29.5, 28.6, 31.2, 29.6, 28, 27.5, 29.2, 30.2, 30.3, 28.2, 29.6, 
27.8, 26.5, 28.4, 28.6, 29.3, 29.8, 28.8, 28.3, 28.4, 27.4,
29.8, 
27.9, 28.5, 27.5, 27.2, 29.7, 28.3, 30.3, 29.7, 25.2, 30.4, 29, 
33.8, 26.3, 28.3, 29.2, 27.7, 30.7, 28, 34.9, 28.2, 26.3, 29.2, 
30.6, 26.2, 31.2, 33.7, 28.7, 33.1, 31.8, 29.8, 27.4, 25.9,
28.7, 
28.4, 21, 26.9, 26.6, 29.5, 30.3, 32.5, 29, 24.6, 28.3, 26.4, 
28.9, 29.3, 31.8, 30.4, 32.4, 29.2, 27.3, 31.2, 30.1, 29.9,
27.1, 
29.8, 27.3, 27.8, 30, 28.8, 28.4, 26.6, 28.9, 29.2, 30.7, 23.1, 
29.5, 31.6, 27.5, 26.2, 28.8, 31, 27.9, 30, 26.7, 29.1, 26.3, 
25.9, 30.4, 25.7, 29.9, 32, 27, 26.8, 31.1, 22, 29.3, 30, 30.1, 
29.7, 27.3, 29.1, 29.6, 26.1, 28.7, 26.3, 28.5, 29.6, 28.9,
30.5, 
24.8, 30.1, 30.7, 29.8, 29.3, 27.3, 32.6, 25.7, 28.6, 27.2,
29.4, 
30), wrist = c(17.1, 18.2, 16.6, 18.2, 17.7, 18.8, 17.7, 18.8, 
18.2, 19.2, 18.5, 19, 17.7, 18.8, 18.2, 16.9, 17.3, 19.3, 18.5, 
18.2, 18.4, 19.9, 16.7, 17.1, 17.6, 17.7, 16.5, 17, 17.2, 17.6, 
18.4, 17.9, 18.8, 18.7, 19.7, 17, 19, 19.4, 21.4, 18.3, 21.4, 
17.4, 18.4, 18.8, 16.1, 18.3, 17.3, 17.9, 16.3, 16.8, 17.3,
17.2, 
16.9, 18.5, 18.5, 18.9, 18.5, 19.2, 18.2, 18.5, 20.2, 18.3,
19.1, 
18.8, 18.4, 18.7, 17.4, 18.7, 18.1, 17.3, 18.6, 18.3, 18.2,
16.9, 
16.8, 18.3, 18.1, 18.8, 18.3, 19, 19, 17.7, 19, 19.2, 18, 18.2, 
18.8, 18.1, 18.8, 18.7, 17.7, 18.8, 18.4, 19.1, 17.8, 20.4,
18.5, 
18.2, 18.2, 18.3, 18.6, 17, 18.4, 19.7, 17.7, 18.8, 18.1, 19.1, 
19.2, 17.3, 18.1, 17.4, 19.8, 17.4, 17.5, 17.3, 18.1, 19.5,
18.5, 
18, 19.5, 18.4, 17.6, 17.6, 18, 17.6, 17.2, 17.4, 18.1, 17.7, 
17.6, 17.1, 17.9, 17.3, 18.1, 17.6, 17.1, 17.7, 17.6, 18.7,
16.6, 
17.8, 17.9, 18.2, 18.3, 17.3, 18.7, 18.4, 16.9, 18.4, 17.8,
19.6, 
17.4, 17.9, 19.4, 17.7, 19.1, 18.6, 16.9, 18.2, 16.5, 19.1,
19.7, 
16.5, 18.5, 19.4, 17.7, 19.8, 18.8, 17.4, 17.7, 16.9, 17.7,
17.8, 
20.1, 16.9, 16.7, 18.4, 18.1, 19.9, 19, 16.5, 17.2, 17.4, 17.7, 
18.2, 20, 19.1, 18.8, 18.5, 17.9, 19.9, 18.7, 18.5, 17.1, 18.8, 
17.4, 16.9, 18.5, 18.8, 18.6, 17.4, 18.7, 18.4, 17.4, 19.4,
17.3, 
18.4, 17.7, 17.6, 17.4, 18.9, 18.6, 19, 18, 18.4, 17.8, 18.6, 
19.2, 17.1, 18.9, 19.6, 17.8, 17, 19.2, 15.8, 18.8, 18.4, 18.8, 
19, 16.9, 19, 18, 17.6, 18.3, 18.3, 19, 18.5, 18.3, 19.1, 16.5, 
19.4, 19.5, 19.5, 18.5, 18.5, 18.8, 18.5, 20.1, 18, 19.8, 20.9
)), .Names = c("neck", "chest", "abdomen", "hip", "thigh",
"knee", 
"ankle", "biceps", "forearm", "wrist"), class = "data.frame",
row.names = 
c(NA, 
-252L))

Hope this helps.



From:   John Kane <jrkrideau at inbox.com>
To:     Pavneet Arora/UK/RoyalSun at RoyalSun
Date:   25/03/2014 18:34
Subject:        RE: [R] Principal Components Loadings



Hi Pavneet,

Your data set did not come through.  The R-help list is likely
to strip 
any attachments other than things like a text file or pdf file
as a 
security feature.  You are better using the ?dput function to
attached the 
data or perhaps use head(dput(mydata), 100) for a sample if it
is a big 
file.

John Kane
Kingston ON Canada


> -----Original Message-----
> From: pavneet.arora at uk.rsagroup.com
> Sent: Tue, 25 Mar 2014 13:41:16 +0000
> To: r-help at r-project.org
> Subject: [R] Principal Components Loadings
> 
> 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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