# BEISPIELE FUER CHERNOV-SCHRANKEN

plot(0:30,dbinom(0:30,30,0.3),ylim=c(0,1),xlab="x",ylab="Wahrscheinlichkeit",main="K sei binomialverteilt mit n=30 und p=0.3",col="blue")
text(20,0.1,"Ws(K=x)",col="blue")
abline(h=0)
dev.copy2eps(file="chernov1.eps")

abline(v=9,lty=2)
text(3,0.6,"EK=9")
dev.copy2eps(file="chernov2.eps")

lines(0:3000/100,pbinom(0:3000/100,30,0.3),col="red")
text(20,0.9,"Ws(K<x)",col="red")
dev.copy2eps(file="chernov3.eps")

lines((1-1:100/100)*0.3*30,exp(-30*0.3*(1:100/100)^2/2),col="green4")
text(3,0.95,"erste Chernov-Schranke",col="green4")
dev.copy2eps(file="chernov4.eps")

plot(0:30,dbinom(0:30,30,0.3),ylim=c(0,1),xlab="x",ylab="Wahrscheinlichkeit",main="K sei binomialverteilt mit n=30 und p=0.3",col="blue")
text(20,0.1,"Ws(K=x)",col="blue")
abline(h=0)
abline(v=9,lty=2)
text(11,0.6,"EK=9")
dev.copy2eps(file="chernov5.eps")

lines(0:3000/100,1-pbinom(0:3000/100,30,0.3),col="red")
text(4,0.9,"Ws(K>x)",col="red")
dev.copy2eps(file="chernov6.eps")

lines((1+1:3000/100)*0.3*30,exp(-30*0.3*(1:3000/100)^2/3),col="green4")
text(17,0.7,"zweite Chernov-Schranke",col="green4")
dev.copy2eps(file="chernov7.eps")


plot(0:30,dbinom(0:30,30,0.3),ylim=c(0.000000000001,1),xlab="x",ylab="Wahrscheinlichkeit",main="K sei binomialverteilt mit n=30 und p=0.3",col="blue",log="y")
text(20,0.01,"Ws(K=x)",col="blue")
abline(h=0)
abline(v=9,lty=2)
text(11,0.6,"EK=9")
lines(0:3000/100,1-pbinom(0:3000/100,30,0.3),col="red")
text(4,0.9,"Ws(K>x)",col="red")
lines((1+1:3000/100)*0.3*30,exp(-30*0.3*(1:3000/100)^2/3),col="green4")
text(17,0.7,"zweite Chernov-Schranke",col="green4")

dev.copy2eps(file="chernov8.eps")

plot(0:100,dbinom(0:100,100,0.15),ylim=c(0,1),xlab="x",ylab="Wahrscheinlichkeit",main="K sei binomialverteilt mit n=100 und p=0.15",col="blue")
text(20,0.1,"Ws(K=x)",col="blue")
abline(h=0)
abline(v=15,lty=2)
text(3,0.6,"EK=15")
lines(0:10000/100,pbinom(0:10000/100,100,0.15),col="red")
text(20,0.9,"Ws(K<x)",col="red")
lines((1-1:100/100)*0.15*100,exp(-100*0.15*(1:100/100)^2/2),col="green4")
text(3,0.95,"erste Chernov-Schranke",col="green4")
dev.copy2eps(file="chernov9.eps")

plot(0:100,dbinom(0:100,100,0.15),ylim=c(0,1),xlab="x",ylab="Wahrscheinlichkeit",main="K sei binomialverteilt mit n=100 und p=0.15",col="blue")
text(20,0.1,"Ws(K=x)",col="blue")
abline(h=0)
abline(v=15,lty=2)
text(11,0.6,"EK=15")
lines(0:100000/100,1-pbinom(0:100000/100,100,0.15),col="red")
text(4,0.9,"Ws(K>x)",col="red")
lines((1+1:10000/100)*0.15*100,exp(-100*0.15*(1:10000/100)^2/3),col="green4")
text(17,0.7,"zweite Chernov-Schranke",col="green4")
dev.copy2eps(file="chernov10.eps")


plot(0:100,dbinom(0:100,100,0.15),ylim=c(0.15^100,1),xlab="x",ylab="Wahrscheinlichkeit",main="K sei binomialverteilt mit n=100 und p=0.15",col="blue",log="y")
text(20,0.01,"Ws(K=x)",col="blue")
abline(h=0)
abline(v=15,lty=2)
text(11,0.6,"EK=15")
lines(0:100000/100,1-pbinom(0:100000/100,100,0.15),col="red")
text(4,0.9,"Ws(K>x)",col="red")
lines((1+1:10000/100)*0.15*100,exp(-100*0.15*(1:10000/100)^2/3),col="green4")
text(17,0.7,"zweite Chernov-Schranke",col="green4")

dev.copy2eps(file="chernov11.eps")

# REGRESSION ZUM MITTELWERT

groessen <- matrix(rnorm(2000),ncol=2)%*%matrix(c(0.05,0.1,0.1,0.05),2)+c(1.7,1.7)

plot(groessen,main="Koerpergroessen",xlim=c(1.3,2.2),ylim=c(1.3,2.2),xlab="Vater",ylab="Sohn")
abline(a=0,b=1,col="grey")
dev.copy2eps(file="regtomed1.eps")


abline(v=10:23/10,col="blue")
dev.copy2eps(file="regtomed2.eps")

sapply(10:22/10,function(x) points(x+0.05,mean(groessen[,2][groessen[,1]>x & groessen[,1]<x+0.1]),col="blue",cex=2,lwd=5))
dev.copy2eps(file="regtomed3.eps")

plot(groessen,main="Koerpergroessen",xlim=c(1.3,2.2),ylim=c(1.3,2.2),xlab="Vater",ylab="Sohn")
abline(a=0,b=1,col="grey")
linie <- coef(lm(groessen[,2]~groessen[,1]))
abline(a=linie[[1]],b=linie[[2]],col="blue")
dev.copy2eps(file="regtomed4.eps")

plot(groessen,main="Koerpergroessen",xlim=c(1.3,2.2),ylim=c(1.3,2.2),xlab="Vater",ylab="Sohn")
abline(a=0,b=1,col="grey")
dev.copy2eps(file="regtomed5.eps")
abline(h=10:23/10,col="red")

sapply(10:22/10,function(x) points(mean(groessen[,1][groessen[,2]>x & groessen[,2]<x+0.1]),x+0.05,col="red",cex=2,lwd=5))
dev.copy2eps(file="regtomed6.eps")

plot(groessen,main="Koerpergroessen",xlim=c(1.3,2.2),ylim=c(1.3,2.2),xlab="Vater",ylab="Sohn")
abline(a=0,b=1,col="grey")
linie <- coef(lm(groessen[,2]~groessen[,1]))
abline(a=linie[[1]],b=linie[[2]],col="blue")
linie <- coef(lm(groessen[,1]~groessen[,2]))
abline(a=-linie[[1]]/linie[[2]],b=1/linie[[2]],col="red")
dev.copy2eps(file="regtomed7.eps")


plot(groessen,main="Koerpergroessen",xlim=c(1.3,2.2),ylim=c(1.3,2.2),xlab="Vater",ylab="Sohn")
abline(a=0,b=1,col="grey")
vektor <- prcomp(groessen)$rotation[,1]
schwerpunkt <- apply(groessen,2,mean)
start <- schwerpunkt-10*vektor
ende <- schwerpunkt+10*vektor
lines(c(start[1],ende[1]),c(start[2],ende[2]),col="purple")
dev.copy2eps(file="regtomed8.eps")


# ANOREXIA-BEISPIEL FUER LINEARE MODELLE

library(MASS)
data(anorexia)
anorexia
ano <- split(anorexia,anorexia$Treat)
plot(ano$Cont$Prewt,ano$Cont$Postwt,
     xlim=c(min(anorexia$Prewt),max(anorexia$Prewt)),
     ylim=c(min(anorexia$Postwt),max(anorexia$Postwt)))
points(ano$CBT$Prewt,ano$CBT$Postwt,col='blue')
points(ano$FT$Prewt,ano$FT$Postwt,col='red')
abline(a=0,b=1,lty="dashed")
summary(lm(Postwt~Prewt,ano$Cont))
abline(a=92.0515,b=-0.1342)
summary(lm(Postwt~Prewt,ano$CBT))
abline(a=15.5772,b=0.8480,col='blue')
summary(lm(Postwt~Prewt,ano$FT))
abline(a=14.8198,b=0.9092,col='red')
summary(lm(Postwt~Prewt+Treat,anorexia))
summary(lm(Postwt~Prewt*Treat,anorexia))