#############
## Cviceni 1
#############

fullmoon <- read.table("fullmoon.txt", header=TRUE)

dim(fullmoon)

fullmoon

summary(fullmoon)

Moon <- factor(fullmoon$Moon, levels=c("Before", "During", "After"))
table(Moon, fullmoon$Moon)
fullmoon$Moon <- Moon

Month <- factor(fullmoon$Month, levels=c("Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"))
table(Month, fullmoon$Month)
fullmoon$Month <- Month

summary(fullmoon)

plot(fullmoon$Admission~fullmoon$Month)
plot(fullmoon$Admission~fullmoon$Moon)

plot(fullmoon$Admission~as.numeric(fullmoon$Month), ylab="Admissions", xlab="Month", main="Admissions by month and moon")
points(fullmoon$Admission[fullmoon$Moon=="Before"]~as.numeric(fullmoon$Month)[fullmoon$Moon=="Before"], pch=19, col="orange")
points(fullmoon$Admission[fullmoon$Moon=="During"]~as.numeric(fullmoon$Month)[fullmoon$Moon=="During"], pch=19, col="firebrick")
points(fullmoon$Admission[fullmoon$Moon=="After"]~as.numeric(fullmoon$Month)[fullmoon$Moon=="After"], pch=19, col="springgreen")

legend(x="topleft", legend=levels(fullmoon$Moon), col=c("orange", "firebrick", "springgreen"), pch=19)

################
## Cviceni 2 a 3
################

model.0 <- lm(Admission~1, data=fullmoon)
summary(model.0)
confint(model.0)

################
## Cviceni 4 a 5
################

model.1 <- lm(Admission~Moon, data=fullmoon)
summary(model.1)
confint(model.1)

# stredni hodnota poctu pacientu pred uplnkem
a <- c(1, 0, 0)
before.est <- t(a)%*%coefficients(model.1) # odhad
before.ci <- t(a)%*%coefficients(model.1) + c(-1, 1)*qt(0.975, df=33)*sqrt(t(a)%*%vcov(model.1)%*%a) # konfidencni interval

# stredni hodnota poctu pacientu behem uplnku
a <- c(1, 1, 0)
during.est <- t(a)%*%coefficients(model.1) # odhad
during.ci <- t(a)%*%coefficients(model.1) + c(-1, 1)*qt(0.975, df=33)*sqrt(t(a)%*%vcov(model.1)%*%a) # konfidencni interval
 
# stredni hodnota poctu pacientu po uplnku
a <- c(1, 0, 1)
after.est <- t(a)%*%coefficients(model.1) # odhad
after.ci <- t(a)%*%coefficients(model.1) + c(-1, 1)*qt(0.975, df=33)*sqrt(t(a)%*%vcov(model.1)%*%a) # konfidencni interval

plot(c(8, 16)~c(1, 3), xlab="Moon", ylab="Admissions", main="Estimated mean admissions by moon", type="n", xaxt="n")
legend(x="topleft", legend=levels(fullmoon$Moon), col=c("orange", "firebrick", "springgreen"), pch=19)

points(1, before.est, pch=19, col="orange")
points(2, during.est, pch=19, col="firebrick")
points(3, after.est, pch=19, col="springgreen")

arrows(x0=1, y0=before.ci[1], x1=1, y1=before.ci[2], lty=2, col="orange", code=3, angle=90, length=0.13)
arrows(x0=2, y0=during.ci[1], x1=2, y1=during.ci[2], lty=2, col="firebrick", code=3, angle=90, length=0.13)
arrows(x0=3, y0=after.ci[1], x1=3, y1=after.ci[2], lty=2, col="springgreen", code=3, angle=90, length=0.13)

# test hypotezy o vlivu uplnku
anova(model.0, model.1)
anova(model.1)