# Daten
SBD1<-c(107,108,104,112,124,102,112,112,100,
        104,122,110,104,102,114,102,120,138,
        144,154,134,166,150,144,130,140,148)
SBD2<-c(124,128,135,124,136,112,135,122,111,
        111,125,122,114,126,137,115,112,113,
        133,166,140,154,170,154,141,154,131)
SBD2<-SBD2-10

# Angabe
summary(SBD1)
summary(SBD2)
ergr<-(lm(SBD2~SBD1))
summary(ergr)
pdf("fig31a.pdf",6,6)
plot(SBD1,SBD2,xlim=c(90,180),ylim=c(90,180))
abline(ergr)
dev.off()
(xbar <- mean(SBD1))
(ybar <- mean(SBD2))
(sx2 <- sum((SBD1-xbar)^2))
(sy2 <- sum((SBD2-ybar)^2))

# Loesung 
# a)
round(sqrt(0.5535),digits=4)

# d)
42.3437 + 0.6446 * 160

# e)
(sxy <- 0.6446*sx2)
(borr <- ( (sy2 - sx2) + sqrt(4*sxy^2 + (sy2 - sx2)^2) ) / (2*sxy))
(aorr <- ybar - borr * xbar)


# f)
regu<-lm(SBD1~SBD2)
summary(regu)

(delta <- round(0.5535/0.6446,digits=4))
(gamma <- round(122.5 - 0.8587 * 121.3, digits=4))
coef(regu)[1]
coef(regu)[2]


round(-gamma/delta + 1/delta * 160, digits=4)

pdf("figA31b.pdf",6,6)
plot(SBD1,SBD2,xlim=c(90,180),ylim=c(90,180))
abline(ergr)
abline(a=-gamma/delta,b=1/delta,col="blue")
dev.off()