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

# Poissonovska regrese

time <- 1:36
# vykresleni dat
plot(time,tab$number,type="p",pch=20,ylab="number of AIDS", xlab="time",main="Poisson regression")

# definice modelu
glm1 <- lm(number ~ time, data = tab)
summary(glm1)
glm2 <- glm(number ~ time, family=poisson("log"), data = tab)
summary(glm2)
glm3 <- glm(number ~ time, family=poisson("sqrt"), data = tab)
summary(glm3)

# vykresleni regresnich krivek
#points(time,fitted(glm1),col=2)
xx<-seq(0,37,by=0.01)
yA.logit<-predict(glm1,list(time=xx),type="response")
lines(xx,yA.logit,col=2,lwd=2)
yB.logit<-predict(glm2,list(time=xx),type="response")
lines(xx,yB.logit,col=3,lwd=2)
yC.logit<-predict(glm3,list(time=xx),type="response")
lines(xx,yC.logit,col=4,lwd=2)
legend("topleft",col=c(2,3,4),lty=c(1,1,1),lwd=c(2,2,2),legend=c("linear","log-linear","square-root"))

# overeni normality residui
plot(glm1,which=2)
shapiro.test(residuals(glm1))
plot(glm2,which=2)
shapiro.test(residuals(glm2))
plot(glm3,which=2)
shapiro.test(residuals(glm3))