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I just ran my first ever PCA, so please excuse any naivety on my part.

As input, I used five years worth of the following:

  • S&P/ASX 200 A-REIT
  • S&P/ASX 200 Consumer Discretionary
  • S&P/ASX 200 Consumer Staples
  • S&P/ASX 200 Energy
  • S&P/ASX 200 Financial-x-A-REIT
  • S&P/ASX 200 Health Care
  • S&P/ASX 200 Industrials
  • S&P/ASX 200 Information Technology
  • S&P/ASX 200 Materials
  • S&P/ASX 200 Resources
  • S&P/ASX 200 Telecommunication Services
  • S&P/ASX 200 Utilities

Using R, I simply ran the following commands:

arc.pca1 <- princomp(sp_sector_data, scores=TRUE, cor=TRUE)
summary(arc.pca1)
plot(arc.pca1)
biplot(arc.pca1)

Summary

Importance of components:
                         Comp.1     Comp.2     Comp.3
Standard deviation     2.603067 1.05203261 0.88394057
Proportion of Variance 0.564663 0.09223105 0.06511258
Cumulative Proportion  0.564663 0.65689405 0.72200662

                           Comp.4     Comp.5     Comp.6
Standard deviation     0.84122312 0.76978259 0.73901015
Proportion of Variance 0.05897136 0.04938044 0.04551133
Cumulative Proportion  0.78097798 0.83035842 0.87586975

                           Comp.7     Comp.8     Comp.9
Standard deviation     0.66409102 0.62338449 0.52003850
Proportion of Variance 0.03675141 0.03238402 0.02253667
Cumulative Proportion  0.91262116 0.94500518 0.96754185

                          Comp.10    Comp.11      Comp.12
Standard deviation     0.45637805 0.42371864 0.0409804189
Proportion of Variance 0.01735674 0.01496146 0.0001399496
Cumulative Proportion  0.98489859 0.99986005 1.0000000000

Loadings

Loadings:
        Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7
RE      -0.235         0.520 -0.533 -0.438  0.355 -0.150
disc    -0.332               -0.125                0.294
staples -0.295  0.226                      -0.211  0.554
energy  -0.332 -0.251         0.172  0.176        -0.130
fin_RE  -0.323               -0.118 -0.130         0.384
health  -0.224  0.465 -0.124 -0.193  0.603  0.537 -0.112
ind     -0.337                                          
IT      -0.224  0.145 -0.757        -0.461        -0.312
mat     -0.329 -0.351         0.295         0.126 -0.116
res     -0.335 -0.350         0.297         0.123 -0.133
telco   -0.161  0.609  0.327  0.609 -0.311        -0.113
util    -0.270  0.160  0.146 -0.256  0.234 -0.694 -0.509

        Comp.8 Comp.9 Comp.10 Comp.11 Comp.12
RE      -0.217                               
disc     0.309  0.567  0.596                 
staples -0.688        -0.141                 
energy         -0.215  0.240  -0.783  -0.165 
fin_RE   0.374 -0.724          0.207         
health                                       
ind      0.398  0.311 -0.743  -0.221         
IT      -0.183                               
mat     -0.127                 0.461  -0.638 
res     -0.123                 0.226   0.752 
telco    0.116                               
util                           0.115         

               Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6
SS loadings     1.000  1.000  1.000  1.000  1.000  1.000
Proportion Var  0.083  0.083  0.083  0.083  0.083  0.083
Cumulative Var  0.083  0.167  0.250  0.333  0.417  0.500

               Comp.7 Comp.8 Comp.9 Comp.10 Comp.11
SS loadings     1.000  1.000  1.000   1.000   1.000
Proportion Var  0.083  0.083  0.083   0.083   0.083
Cumulative Var  0.583  0.667  0.750   0.833   0.917

               Comp.12
SS loadings      1.000
Proportion Var   0.083

Scree Plot

enter image description here

Biplot

enter image description here

Is this useful?

Am I right in assuming that these indices are correlated with each other?

Does the biplot show some sort of clustering?

What if anything, does any of this mean?

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  • $\begingroup$ It's not entirely clear what you are asking. Surely you had a reason to use PCA? What are you trying to learn? Did you use PCA without knowing what it does? $\endgroup$
    – Marc Claesen
    Oct 20, 2013 at 13:40
  • $\begingroup$ Honestly, I was hoping that there would be two or three components and that certain industry sectors would correlated with each other. I don't have a pressing reason to do a PCA, other than curiosity. $\endgroup$
    – CuriousCat
    Oct 20, 2013 at 13:46
  • $\begingroup$ @CuriousCat, Be curious and search this site for "pca biplot". There is also tags pca and biplot. $\endgroup$
    – ttnphns
    Oct 20, 2013 at 17:03
  • $\begingroup$ Since you have outliers in the data set, they might be dominating your variances. Judging from your plot, the data is a single large blob only, and there is no structure to be seen in here. You may need to do more manual preprocessing and data cleaning. $\endgroup$
    – Has QUIT--Anony-Mousse
    Oct 21, 2013 at 12:28

1 Answer 1

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PCA tries to project your data onto a new set of dimensions where the variances in your data are captured such that you can classify/cluster them visually or by using a hopefully simple algorithm.

The variance plot tells you how much the new set of dimensions capture variances in decreasing order. Biplot is the projection of your data on the first two principal components (where the variances are the highest).

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  • $\begingroup$ Can you please tell me more about the red lines on the biplot. Some of them appear to be grouped together. Does this mean anything. For example, energy, resources and materials appear to be going in a similar direction. $\endgroup$
    – CuriousCat
    Oct 20, 2013 at 14:06
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    $\begingroup$ I am not very familiar with R and never have I used the vector representation. The R documentation tells the following about the direction of arrows: cc.oulu.fi/~jarioksa/softhelp/vegan/html/biplot.rda.html $\endgroup$
    – Zoran
    Oct 20, 2013 at 14:56

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