tab <- read.csv2 (file = "beetle.csv")
summary (tab)

tab$proportions <- tab$killed / tab$population

# Logisticka regrese
# Vykresleni dat
plot(tab$dose, tab$proportions,pch=20,xlab="CS2",ylab="umrtnost")

# definice GLM modelu
glmmod1 <- glm(formula = cbind(killed, population - killed) ~ dose, family = binomial(logit),data = tab)
summary(glmmod1)

# vykresleni regresni krivky
t <- seq(from = min(tab$dose), to=max(tab$dose), by=0.001)
lines(t,predict(glmmod1,data.frame(dose=t),type="response"),col="red")

# overeni normality residui
plot(glmmod1,which=2)
shapiro.test(residuals(glmmod1))

# Probitovy model
# Vykresleni dat
plot(tab$dose,tab$proportions,pch=20,xlab="CS2",ylab="umrtnost")

# definice GLM modelu
glmmod2 <- glm(formula = cbind(killed, population - killed) ~ dose, family = binomial(probit),data = tab)
summary(glmmod2)

# vykresleni regresni krivky
t <- seq(from=min(tab$dose),to=max(tab$dose),by=0.001)
lines(t,predict(glmmod2,data.frame(dose=t),type="response"),col="red")

# overeni normality residui
plot(glmmod2,which=2)
shapiro.test(residuals(glmmod2))

# komplementarni log-log
# Vykresleni dat
plot(tab$dose,tab$proportions,pch=20,xlab="CS2",ylab="umrtnost")

# definice GLM modelu
glmmod3 <- glm(formula = cbind(killed, population - killed) ~ dose, family = binomial(link="cloglog"),data = tab)
summary(glmmod3)

# vykresleni regresni krivky
t <- seq(from=min(tab$dose),to=max(tab$dose), by=0.001)
lines(t,predict(glmmod3,data.frame(dose=t),type="response"),col="red")

# overeni normality residui
plot(glmmod3,which=2)
shapiro.test(residuals(glmmod3))

# vsechny tri modely
plot(tab$dose, tab$proportions,pch=20,xlab="CS2",ylab="umrtnost")
lines(t,predict(glmmod1,data.frame(dose=t),type="response"),col="red")
lines(t,predict(glmmod2,data.frame(dose=t),type="response"),col="green")
lines(t,predict(glmmod3,data.frame(dose=t),type="response"),col="blue")