Homework SourseA principla component analysis was done on 200 crabs The mea
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 |
Solution
Variance explained by the first two components
= (0.289 + 0.685)/(0.289+0.685-0.175+0.126+0.439)
= 0.7141
= 71.41%
b.)
