# Statistik 2 - Blatt 11 - Aufgabe 3

# Daten einlesen
daten <- read.table("C:\\challenger.txt", header = T)

# a) Logit-Modell
logitModell <- glm(daten$Ausfall ~ daten$Temperatur, family = binomial(link = logit))
summary(logitModell)

# b) Prognose der Ausfallwahrscheinlichkeit bei 31 °F
beta0 <- as.vector(coef(logitModell))[1]
beta1 <- as.vector(coef(logitModell))[2]
print(exp(beta0 + beta1 * 31) / (1 + exp(beta0 + beta1 * 31)))

# c) Probit-Modell
probitModell <- glm(daten$Ausfall ~ daten$Temperatur, family = binomial(link = probit))
summary(probitModell)

# Prognose der Ausfallwahrscheinlichkeit bei 31 °F
beta2 <- as.vector(coef(probitModell))[1]
beta3 <- as.vector(coef(probitModell))[2]
print(pnorm(beta2 + beta3 * 31))

# d) Kurven plotten
s <- rep(0, 1000)
min <- 29
max <- 91
for (i in 1:1000) {
	s[i] <- min + (i - 1) * (max - min) / 1000
}
w1 <- exp(beta0 + beta1 * s) / (1 + exp(beta0 + beta1 * s))
plot(s, w1, xlab = "Temperatur in °F", ylab = "Ausfallwahrscheinlichkeit", type = "l")
w2 <- pnorm(beta2 + beta3 * s)
lines(s, w2, lty = 2)
points(daten$Temperatur, daten$Ausfall, pch = 8)
legend(x = 30, y = 0.2, legend = c("Logit-Modell", "Probit-Modell"), lty = c(1, 2))