# Prvni priklad - index determinace
# nacteni dat
load("cviceni4.RData")
x <- data4$pr1$x
y <- data4$pr1$y
yhat <- data4$pr1$yhat

# vypocet - 1. zpusob
jmen <- mean((y-mean(y))^2)
ID <- mean((yhat-mean(y))^2)/jmen
ID

# vypocet - 2. zpusob
residuals <- y-yhat
cit <- mean(residuals^2)
ID <- 1-cit/jmen
ID

# Druhy priklad - mnohonasobna korelace

vyb <- data4$pr2
y <- vyb$Ozone
X<-vyb[,-1]
RXX <- cor(X,X)
r <- cor(y,X)
ir<-solve(RXX)
r%*%ir%*%t(r)

#druhy zpusob
R<-cor(vyb,vyb)
(1-det(R)/det(RXX))


# Treti priklad - parcialni korelace pomoci prikazu
# baliky
#install.packages("ggm")
library(ggm)
pcor(c("Ozone","Solar.R","Wind","Temp"),var(vyb))
pcor(c("Ozone","Wind","Solar.R","Temp"),var(vyb))
pcor(c("Ozone","Temp","Wind","Solar.R"),var(vyb))

# parcialni Ozone X Solar.R s vyloucenim ost.
rcit <- R[-1,-2]
det(rcit)/sqrt(det(R[-1,-1])*det(R[-2,-2]))

# -----------------------------------------------------------------