#Übung 4

#Aufgabe 1
#a)
service <- read.table("http://stat.ethz.ch/Teaching/Datasets/softdrink.dat", header=T)
#y=servicezeit, x1=# nachzufüllende produkte, x2=weg: servicewagen automat
service
summary(service)
mod_1 <- lm(formula = y ~ x1 + x2,data=service)
summary(mod_1)
#b)
newdata <- data.frame(x1=8,x2=275)
pred <- predict(mod_1,newdata=newdata,interval="prediction")
pred
mod_1$coefficients[1] + 8*mod_1$coefficients[2] + 275*mod_1$coefficients[3]
#predict macht also das was es soll
#c)
par(mfrow = c(2,2))
plot(mod_1)
#normal q-q plot eine art zwei geteilt, 9 (evtl. 20, 22 auch noch) scheint eine einflussreiche messung zu sein.
service_neu <- service[-9,]
mod_2 <- lm(formula = y ~ x1 + x2,data=service_neu)
summary(mod_2)
plot(mod_2)
pred_1 <- predict(mod_2,newdata=newdata,interval="prediction")
pred_1
#wert kann genauer geschätzt werden

#Aufgabe 2
schueler <- read.table("http://stat.ethz.ch/Teaching/Datasets/concept.dat", header=T)
summary(schueler)
#a)
attach(schueler)
mod_1 <- lm(formula = gpa ~ iq + alter + sex + total + c1 + c2 + c3 + c4 + c5 + c6, data=schueler)
summary(mod_1)
#nur iq ist signifikant
stepback <- step(mod_1,direction="backward")
formula(stepback)
modback <- lm(formula(stepback))
summary(modback)
ausgangsm <- lm(gpa~1)
stepforward <- step(ausgangsm, scope=formula(mod_1),direction="forward")
modfrow <- lm(formula(stepforward))
formula(stepforward)
summary(modfrow)
#b)
par(mfrow=c(2,2))
plot(mod_1)
#22,48,51 evtl. 41 sind ausreisser
entfernen <- c(22,48,51)
schueler_neu <- schueler[-entfernen,]
attach(schueler_neu)
mod_2 <- lm(gpa ~ iq + alter + sex + total + c1 + c2 + c3 + c4 + c5 + c6)
summary(mod_2)
par(mfrow=c(2,2))
plot(mod_2)

#Aufgabe 3
#a)
chriket <- read.table("http://stat.ethz.ch/Teaching/Datasets/cricket.dat", header=T)
attach(chriket)
mod_1 <- lm(formula = y ~ x1 + x2 + x3 + x4 + I(x1^2) + I(x4^2) + I(x1*x4))
summary(mod_1)
#b)
#die quadratischen terme sind nicht signifikant, mal rausnehmen und sehen was passiert
mod_2 <- lm(formula = y ~ x1 + x2 + x3 + x4 + I(x1*x4))
summary(mod_2)
#x1 wird nun signifikant
scopeback <- list(lower=y~x1+x2+x4+I(x1*x4), upper=formula(mod_1))
modback <- step(mod_1, scope=scopeback, direction="backward")
modback <- lm(formula(modback))
amod <- lm(y ~ x1 + x2 + x4 + I(x1*x4))
scopeforward <- list(lower = y ~ x1 + x2 + x4 + I(x1*x4), upper=formula(mod_1))
modforward <- step(amod, scope=scopeforward, direction="forward")
#c)
mod_3 <- lm(formula = y ~ x1 + x2 + x4 + I(x1*x4) + I(x2^2) + I(x1*x2) + I(x2*x4))
summary(mod_3)
#werden sehr signifikant
mod_4 <- lm(y ~ x1 + x2 + x4 + I(x1*x4) + I(x2^2) + I(x1*x2) + I(x2*x4))
scopeback <- list(lower = y ~ x1 + x2 + x4 + I(x1*x4), upper = formula(mod_4))
modback_2 <- step(mod_4, scope=scopeback, direction="backward")
modback_2 <- lm(formula(modback_2))
amod <- lm(y ~ x1 + x2 + x4 + I(x1*x4))
scopeforward <- list(lower = y ~ x1 + x2 + x4 + I(x1*x4), upper=formula(mod_4))
modforward_2 <- step(amod, scope=scopeforward, direction="forward")
par(mfrow=c(2,2))
plot(mod_4,which=c(1,4))
plot(modback_2,which=c(1,4))
plot(modforward_2,which=c(1,4))
summary(mod_4)
summary(modback_2)
summary(modforward_2)

#d)
#ausreiser 1,4,13
chriket <- chriket[-c(1,4,13),]
attach(chriket)
mod_4 <- lm(y ~ x1 + x2 + x4 + I(x1*x4) + I(x2^2) + I(x1*x2) + I(x2*x4))
scopeback <- list(lower = y ~ x1 + x2 + x4 + I(x1*x4), upper = formula(mod_4))
modback_2 <- step(mod_4, scope=scopeback, direction="backward")
modback_2 <- lm(formula(modback_2))
amod <- lm(y ~ x1 + x2 + x4 + I(x1*x4))
scopeforward <- list(lower = y ~ x1 + x2 + x4 + I(x1*x4), upper=formula(mod_4))
modforward_2 <- step(amod, scope=scopeforward, direction="forward")
par(mfrow=c(2,2))
plot(mod_4,which=c(1,4))
plot(modback_2,which=c(1,4))
plot(modforward_2,which=c(1,4))
summary(mod_4)
summary(modback_2)
summary(modforward_2)
#etwa das gleiche