# R - Principal Component Analysis

## Function

````prcomp `
```

Package stats

## Steps

### Perform the analysis

````pcaData = prcomp(USArrests, scale=TRUE)`
```

where:

• scale=TRUE will standardize the variables in order to take into account the different unity.

### Review the principal component data

• The data
````pcaData`
```
``````Standard deviations:
[1] 1.5748783 0.9948694 0.5971291 0.4164494

Rotation:
PC1        PC2        PC3         PC4
Murder   -0.5358995  0.4181809 -0.3412327  0.64922780
Assault  -0.5831836  0.1879856 -0.2681484 -0.74340748
UrbanPop -0.2781909 -0.8728062 -0.3780158  0.13387773
Rapee    -0.5434321 -0.1673186  0.8177779  0.08902432```
```
• The variables associated (names)
````names(pcaData)`
```
````[1] "sdev"     "rotation" "center"   "scale"    "x"`
```
• Unclass will show the data :)
````unclass(pcaData)`
```
``````\$sdev
[1] 1.5748783 0.9948694 0.5971291 0.4164494

\$rotation
PC1        PC2        PC3         PC4
Murder   -0.5358995  0.4181809 -0.3412327  0.64922780
Assault  -0.5831836  0.1879856 -0.2681484 -0.74340748
UrbanPop -0.2781909 -0.8728062 -0.3780158  0.13387773
Rapee    -0.5434321 -0.1673186  0.8177779  0.08902432

\$center
Murder  Assault UrbanPop     Rapee
7.788  170.760   65.540   21.232

\$scale
Murder   Assault  UrbanPop      Rapee
4.355510 83.337661 14.474763  9.366385

\$x
PC1         PC2         PC3          PC4
Alabama        -0.97566045  1.12200121 -0.43980366  0.154696581
Alaska         -1.93053788  1.06242692  2.01950027 -0.434175454
Arizona        -1.74544285 -0.73845954  0.05423025 -0.826264240
Arkansas        0.13999894  1.10854226  0.11342217 -0.180973554
California     -2.49861285 -1.52742672  0.59254100 -0.338559240
Colorado       -1.49934074 -0.97762966  1.08400162  0.001450164
Connecticut     1.34499236 -1.07798362 -0.63679250 -0.117278736
Delaware       -0.04722981 -0.32208890 -0.71141032 -0.873113315
Florida        -2.98275967  0.03883425 -0.57103206 -0.095317042
......................................```
```

### Plot the data

````biplot(pcaData, scale=0)`
```