5.1 Robuste Gerade nach Tukey

# robuste Regressionsgerade

x <- c(0.5,0.9,1,1.2,2.3,2.6,2.8,3.3,3.9,4.2,4.4,6.5)
y <- c(0.5,0.9,0.7,1.3,1.5,2.0,2.5,2.1,2.6,3.4,3.2,1.1)

# Konstruktion TUKEY:
pdf("robline.pdf",width=5,height=5)
par(mar=c(4,4,1,1))
plot(x,y,cex.lab=1.3)
xord <- order(x)
xs <- x[xord]
ys <- y[xord]
points(median(xs[1:4]),median(ys[1:4]),pch=3,cex=1.3)
points(median(xs[5:8]),median(ys[5:8]),pch=3,cex=1.3)
points(median(xs[9:12]),median(ys[9:12]),pch=3,cex=1.3)
legend(0.5,3.4,c("Datenpunkt","Gruppenmedian"),pch=c(1,3),cex=1.3)
dev.off()

# robuste Regressionsgerade

x <- c(0.5,0.9,1,1.2,2.3,2.6,2.8,3.3,3.9,4.2,4.4,6.5)
y <- c(0.5,0.9,0.7,1.3,1.5,2.0,2.5,2.1,2.6,3.4,3.2,1.1)

# Gesamter Algo von TUKEY:
pdf("roblineall.pdf",width=5,height=5)
par(mar=c(4,4,1,1))
plot(x,y,cex.lab=1.3)
xord <- order(x)
xs <- x[xord]
ys <- y[xord]
xl <- median(xs[1:4])
yl <- median(ys[1:4])
xm <- median(xs[5:8])
ym <- median(ys[5:8])
xr <- median(xs[9:12])
yr <- median(ys[9:12])
points(xl,yl,pch=3,cex=1.3)
points(xm,ym,pch=3,cex=1.3)
points(xr,yr,pch=3,cex=1.3)

b <- (yr-yl)/(xr-xl)
a <- 1/3*(yl-b*(xl-xm)+ym+yr-b*(xr-xm))
abline(a-b*xm,b)
r <- ys-(a+b*(xs-xm))

yl <- median(r[1:4])
ym <- median(r[5:8])
yr <- median(r[9:12])
b1 <- (yr-yl)/(xr-xl)
a1 <- 1/3*(yl-b*(xl-xm)+ym+yr-b*(xr-xm))
bneu <- b+b1
aneu <- a+a1
abline(aneu-bneu*xm,bneu)
r1 <- (ys-(aneu+(bneu)*(xs-xm)))

yl <- median(r1[1:4])
ym <- median(r1[5:8])
yr <- median(r1[9:12])
b1 <- (yr-yl)/(xr-xl)
a1 <- 1/3*(yl-b*(xl-xm)+ym+yr-b*(xr-xm))
bneu <- bneu+b1
aneu <- aneu+a1
abline(aneu-bneu*xm,bneu)
dev.off()