#===========================================================================
# Zusatzmaterial zu Übungsblatt 9
# Statistik 4 für Nebenfachstudierende
# SoSe 2017
#
# Datum: 13.07.2017
# Autor: Micha Schneider
#=============================================================================

## Aufgabe 18

# data:
x <- matrix(c(23,25,46,55,51,100,60,84,34,40),nrow=2)
colnames(x) <- c("Person 1","Person 2","Person 3","Person 4","Person 5")
rownames(x) <- c("Alter","Einkommen")

# euclidean distances:
xd <- dist(t(x), method = "euclidean")
xd

## Single Linkage

# clustering:
SL <- hclust(xd, method="single")

# plot of dendrogram:
plot(SL)

# heights:
SL$height

## Complete Linkage
CL <- hclust(xd, method="complete")
plot(CL)
CL$height


## Aufgabe 19

# data
x <- matrix(c(81.1,64.9,79.6,81,85,1.29,2.97,2.02,2.7,1.33), ncol=2)
rownames(x) <- c("Deutschland","Indien","Indonesien","Israel","Japan")
colnames(x) <- c("Lebenserwartung","KinderproFrau")
x
cov(x)

# Standardisierung (-> mean = zero, variance = 1)
xs <- cbind(scale(x[,1]),scale(x[,2]))
(x[,1]-mean(x[,1]))/sqrt(cov(x)[1,1]) # per Hand
(x[,2]-mean(x[,2]))/sqrt(cov(x)[2,2])

# euclidean distances:
xd <- round(dist(xs),2)
round(xd,1)

 # clustering:
CL2 <- hclust(xd, method="complete")
plot(CL2, hang=-1)
CL2$height