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# Blatt 10 #
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#aufgabe 1

Cars <- read.table(".../Cars.txt",header=T,sep="\t",quote="")

attach(Cars)

#a
mod1<-lm(City.Miles.Per.Gallon ~ Weight..Pounds.)
mod1
summary(mod1)

mod2<-lm(City.Miles.Per.Gallon ~ Horsepower)
mod2
summary(mod2)

par(mfrow = c(1,2))

plot(Weight..Pounds., City.Miles.Per.Gallon, pch = 19)
abline(mod1)

plot(Horsepower, City.Miles.Per.Gallon, pch = 19)
abline(mod2)

#Gibt sehr starke Ausreisser, Linearitaet des Modells verletzt (sehr schlecht)

#b
JavaGD()
par(mfrow = c(2,2))
plot(mod1, pch = 19)

JavaGD()
par(mfrow = c(2,2))
plot(mod2, pch = 19)

#c

cmpg<-1/City.Miles.Per.Gallon

mod3<-lm(cmpg ~ Weight..Pounds.)
mod3
summary(mod3)

JavaGD()
par(mfrow = c(2,2))
plot(mod3, pch = 19)

#plot(Weight..Pounds., cmpg, pch = 19)

#Transformation fuehrt zu linearem Zusammenhang


#Durch Tranformation wird Komplexitaet groesser, Interpretation kann erschwert werden, Definiertheit nicht gesichert

#aufgabe 4

#a
qwilcox(0.975,11,13)

qwilcox(0.95,11,13)

1-pwilcox(129,13,11)

#b
mu<-11* 13 / 2
sigma<-sqrt(11 * 13 * (11+13+1) /12)

1-pnorm(129, mu, sigma)