setwd('')

# 1

data <- read.table('newborns.txt', header=TRUE)

x<-na.omit(data$weight.C)

# 1a)
mu<-mean(x) # stredni hodnotu odhadneme pomoci prumeru
sigma_squared<-var(x) # rozptyl odhadneme pomoci vyberoveho rozptylu
sigma<-sqrt(sigma_squared) # a tedy smerodatnou odchylku  pomoci vyberove smerodatne odchylky

# 1b)
hist(x, prob = T, density = 30,
col = 'blue', xlab = 'porodni hmotnost',ylab = 'hustota', main = '')

lines(density(x), col = 'blue', lwd = 2)
curve(dnorm(x,mu,sigma),add=T,col='red',lwd=2)
legend('topleft',c('normalni rozdeleni','jadrovy odhad'),col=c('red','blue'),lwd=2)

plot(ecdf(x),col = 'blue', xlab = 'porodni hmotnost',ylab = 'distribucni funkce', main = '',verticals = TRUE,do.points = FALSE,lwd=2)
curve(pnorm(x,mu,sigma),add=T,col='red',lwd=2)
legend('topleft',c('normalni rozdeleni','empiricka distribucni funkce'),col=c('red','blue'),lwd=2)



###########################################################
# 4
###########################################################

data <- read.table('head.txt', header=TRUE)
x<-data$head.L
y<-data$head.W

plot(x,y,xlab='delka hlavy',ylab='sirka hlavy',asp=1)

library(mvtnorm)

mu1<-mean(x)
mu2<-mean(y)

sigma1_squared<-var(x)
sigma2_squared<-var(y)
rho<-cor(x,y)

sigma12<-rho*sqrt(sigma1_squared*sigma2_squared)
cov(x,y)

mu<-c(mu1,mu2) # odhad vektoru strednich hodnot
sigma<-matrix(c(sigma1_squared,sigma12,sigma12,sigma2_squared),nrow=2) # odhad kovariancni matice

# vytvorime si pomocnou mrizku pro vypocet hustoty
xx<-seq(165,215,by=0.5)
yy<-seq(130,170,by=0.5)

# a v kazdem jejim bode spocitame hodnotu odhadnute hustoty
f<-matrix(0, nrow=length(xx), ncol=length(yy))
for(i in 1:length(xx)){
for(j in 1:length(yy)){
f[i,j] <- dmvnorm(c(xx[i],yy[j]),mu,sigma)
}}

contour(xx, yy, f, asp = T, drawlabels = F, nlevels = 11,
xlab='delka hlavy',ylab='sirka hlavy',col='red')
points(x,y)

# na zaver jeden 3D graf
library(GA)

persp3D(xx, yy, f, xlab = 'delka hlavy',ylab = 'sirka hlavy', zlab = 'f(x, y)')

# muzeme jej trochu vylepsit
persp3D(xx, yy, f, phi = 30, theta = 5, ticktype = 'simple',xlab = 'delka hlavy',
ylab = 'sirka hlavy', zlab = 'f(x, y)', col.palette = terrain.colors, border = 'black')