foot <- read.table("DATA/lrm-foot.txt",header=T)
summary(foot)

library(car)

dataEllipse(foot$foot.L, foot$body.H, level=0.95, xlab='Delka chodidla (mm)',
            ylab='Telesna vyska (mm)', xlim=c(210,300), ylim=c(1500, 1950))

cor.test(foot$foot.L, foot$body.H, method='pearson')

neck <- read.table("DATA/cneck.txt",header=T)
summary(neck)

plot(neck[,3:8])

cov(neck[,3:8], method='pearson')

cor(neck[,3:8], method='pearson')

library(Hmisc)
rcorr(as.matrix(neck[,3:8]), type='pearson')

m1 <- lm(neck.C ~ body.H + waist.C + hip.C + antb.C, data=neck)
y.res <- m1$residuals
m2 <- lm(body.W ~ body.H + waist.C + hip.C + antb.C, data=neck)
z.res <- m2$residuals

r_yz.x <- cor(y.res,z.res)
r_yz.x

n <- nrow(neck)
k <- 4
t.obs <- r_yz.x*sqrt(n-k-2)/sqrt(1-r_yz.x^2)
t.obs

qt(0.975,n-k-2)

2*(1-pt(abs(t.obs), n-k-2))

library(ppcor)
pcor(neck[,3:8], method='pearson')

cor.yx <- cor(neck$neck.C, neck[,3:7], method='pearson')
cor.yx

cor.xx <- cor(neck[,3:7], method='pearson')
cor.xx

r.yx <- sqrt(cor.yx %*% solve(cor.xx) %*% t(cor.yx))
r.yx

model <- lm(neck.C ~ body.W + body.H + waist.C + hip.C + antb.C, data=neck)
y.odhad <- model$fitted.values
r.yx <- cor(neck$neck.C, y.odhad, method='pearson')
r.yx

ID <- summary(model)$r.squared
sqrt(ID)

n <- nrow(neck)
k <- 5
F.obs <- (n-k-1)/k * r.yx^2/(1-r.yx^2)
F.obs
## [1] 97.33264
qf(0.95,df1=k, df2=n-k-1)

summary(model)