#############
## 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)

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

############
## Cviceni 5
############

mu <- mean(fullmoon$Admission)
sst <- sum((fullmoon$Admission-mu)^2)
mu.before <- mean(fullmoon$Admission[fullmoon$Moon=="Before"])
mu.during <- mean(fullmoon$Admission[fullmoon$Moon=="During"])
mu.after <- mean(fullmoon$Admission[fullmoon$Moon=="After"])
ssa <- 12*(mu.before-mu)^2+12*(mu.during-mu)^2+12*(mu.after-mu)^2
sse <- sum((fullmoon$Admission[fullmoon$Moon=="Before"]-mu.before)^2)+sum((fullmoon$Admission[fullmoon$Moon=="During"]-mu.during)^2)+sum((fullmoon$Admission[fullmoon$Moon=="After"]-mu.after)^2)

mu
mu.before
mu.during
mu.after
ssa
sse
sst
ssa/2
sse/33
sst/35
sqrt(sse/33)

summary(model.0)
mu
sqrt(sst/35)
t.test(fullmoon$Admission)

summary(model.1)
mu.before
mu.during-mu.before
mu.after-mu.before
sqrt(sse/33)
1-sse/sst
1-(sse/33)/(sst/35)
(ssa/2)/(sse/33)
1-pf((ssa/2)/(sse/33), df1=2, df2=33)

anova(model.1)
ssa
ssa/2
sse
sse/33
(ssa/2)/(sse/33)
1-pf((ssa/2)/(sse/33), df1=2, df2=33)

anova(model.0, model.1)
sst
sse 
ssa
(ssa/2)/(sse/33)
1-pf((ssa/2)/(sse/33), df1=2, df2=33)