A principla component analysis was done on 200 crabs. The measurements were FL=f

Question

A principla component analysis was done on 200 crabs. The measurements were FL=frontal lobe size, RW=rear width, CL=carpace length, CW=carapace width, and BD=body depth. The results are shown:

a) What fraction of the total variance in these variables is accounted for by the first two principal cmponenets together?

b) suppose a crab has measurements FL=14, RW=12, CL=28, CW=30, BD=12. What are its first two principal components?

>crabs.prcp

Standard deviations:[1] 11.862 1.139 1.000 0.368 0.279

Rotation:

PC1 PC2 PC3 PC4 PC5 FL 0.289 0.323 -0.507 0.734 0.125 RW 0.197 0.685 0.414 -0.148 -0.141 CL 0.599 -0.198 -0.175 0.144 -0.743 CW 0.662 -0.288 0.491 0.126 0.471 BD 0.284 0.16 -0.547 -0.634 0.439

Explanation / Answer

a) What fraction of the total variance in these variables is accounted for by the first two principal cmponenets together?

11.862 + 1.139 + 1.000+ 0.368 +0.279= 14.648 / 5 = 2.9296

What are its first two principal components?

pC1 and pC2

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