rm(list=ls(all=T))

# Daten einlesen
data1 <- read.table("C:/Lehre/Wirtschaftsstatistik 2012/Blatt4/data1.txt", header = TRUE)
data2 <- read.table("C:/Lehre/Wirtschaftsstatistik 2012/Blatt4/data2.txt", header = TRUE)
data3 <- read.table("C:/Lehre/Wirtschaftsstatistik 2012/Blatt4/data3.txt", header = TRUE)


#Berechnet den Rang eines Vektors
rankFkt <- function(x) {
	s<-sort(x)
	res<-rep(0,length(x))
	for(i in 1:length(x)){
		for(j in 1:length(x)){	
			if(x[i] == s[j]){
				res[i] <- j		
			}
		}
	}	

	return(res)
}


# empirische Kovarianz
empCov <- function(x, y) {
	s <- sum((x - mean(x)) * (y - mean(y)))
	s <- s / (length(x) - 1)
	return(s)
}

# empirischer Korrelationskoeffizient
empCorr <- function(x, y) {
	r <- empCov(x, y) / sqrt(empCov(x, x) * empCov(y, y))
	return(r)
}

# Rang-Korrelationskoeffizient
rankCorr <- function(x, y) {
	r <- 1 - 6 * sum((rank(x) - rank(y))^2) / ((length(x)^2 - 1) * length(x))
	return(r)
}

# Alternative Rang-Korrelationskoeffizient
rankCorr2 <- function(x, y) {
	r <- 1 - 6 * sum((rankFkt(x) - rankFkt(y))^2) / ((length(x)^2 - 1) * length(x))
	return(r)
}

# 1. Datensatz
plot(data1)
empCorr(data1$X, data1$Y)
rankCorr(data1$X, data1$Y)
rankCorr2(data1$X, data1$Y)

# 2. Datensatz
plot(data2)
empCorr(data2$X, data2$Y)
rankCorr(data2$X, data2$Y)

# 3. Datensatz
plot(data3)
empCorr(data3$X, data3$Y)
rankCorr(data3$X, data3$Y)