PCA.R

#set wd
setwd("C:/Users/sharl/Desktop/USF/Fall 2021/LIS 4805 - Predictive Analytics")

#Use the 'USArrest' data (in R):
dimnames(USArrests)

## [[1]]
##  [1] "Alabama"        "Alaska"         "Arizona"        "Arkansas"      
##  [5] "California"     "Colorado"       "Connecticut"    "Delaware"      
##  [9] "Florida"        "Georgia"        "Hawaii"         "Idaho"         
## [13] "Illinois"       "Indiana"        "Iowa"           "Kansas"        
## [17] "Kentucky"       "Louisiana"      "Maine"          "Maryland"      
## [21] "Massachusetts"  "Michigan"       "Minnesota"      "Mississippi"   
## [25] "Missouri"       "Montana"        "Nebraska"       "Nevada"        
## [29] "New Hampshire"  "New Jersey"     "New Mexico"     "New York"      
## [33] "North Carolina" "North Dakota"   "Ohio"           "Oklahoma"      
## [37] "Oregon"         "Pennsylvania"   "Rhode Island"   "South Carolina"
## [41] "South Dakota"   "Tennessee"      "Texas"          "Utah"          
## [45] "Vermont"        "Virginia"       "Washington"     "West Virginia" 
## [49] "Wisconsin"      "Wyoming"       
## 
## [[2]]
## [1] "Murder"   "Assault"  "UrbanPop" "Rape"

apply(USArrests, 2, mean)

##   Murder  Assault UrbanPop     Rape 
##    7.788  170.760   65.540   21.232

apply(USArrests, 2, var)

##     Murder    Assault   UrbanPop       Rape 
##   18.97047 6945.16571  209.51878   87.72916

pca.out = prcomp(USArrests, scale = T)
pca.out

## Standard deviations (1, .., p=4):
## [1] 1.5748783 0.9948694 0.5971291 0.4164494
## 
## Rotation (n x k) = (4 x 4):
##                 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
## Rape     -0.5434321 -0.1673186  0.8177779  0.08902432

names(pca.out)

## [1] "sdev"     "rotation" "center"   "scale"    "x"

biplot(pca.out, scale = 0)

biplot(pca.out, scale = 0, cex = 0.6) #make font smaller