Laboratorio Capitulo 10.4

states=row.names(USArrests)
states

##  [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"

names(USArrests)

## [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

pr.out=prcomp(USArrests, scale=TRUE)

names(pr.out)

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

pr.out$center

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

pr.out$scale

##    Murder   Assault  UrbanPop      Rape 
##  4.355510 83.337661 14.474763  9.366385

pr.out$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
## Rape     -0.5434321 -0.1673186  0.8177779  0.08902432

dim(pr.out$x)

## [1] 50  4

biplot(pr.out, scale=0)

pr.out$rotation=-pr.out$rotation
pr.out$x=-pr.out$x
biplot(pr.out, scale=0)

pr.out$sdev

## [1] 1.5748783 0.9948694 0.5971291 0.4164494

pr.var=pr.out$sdev^2
pr.var

## [1] 2.4802416 0.9897652 0.3565632 0.1734301

pve=pr.var/sum(pr.var)
pve

## [1] 0.62006039 0.24744129 0.08914080 0.04335752

plot(pve, xlab="Principal Component", ylab="Proportion of Variance Explained", ylim=c(0,1), type='b')

plot(cumsum(pve), xlab="Principal Componenet", ylab="Cumulative Proportion of Variance Explained", ylim=c(0,1),type='b')

a=c(1,2,8,-3)
cumsum(a)

## [1]  1  3 11  8