#setwd('C:/Disk D/ND-Skola/02-Vyuka/01-Aplikovaná statistika/Data_cviceni_txt')
library(rgl)
#==========================================================================================
data<-read.delim('ocel.txt',sep='',dec='.')
head(data)
pevnost<-data$mez_pevnosti
plasticita<-data$mez_plasticity
n<-length(pevnost)
(Sturges<-round(1+3.3*log10(n),digits=0))
range(pevnost)

dh_pl<-c(30,50,70,90,110,130,150)
hh_pl<-c(50,70,90,110,130,150,170)

dh_pev<-c(50,70,90,110,130,150,170)
hh_pev<-c(70,90,110,130,150,170,190)
m<-length(dh_pl)

VR<-function(X,dh,hh){
  m<-length(dh)
  nj<-rep(0,m)
  for(j in 1:m){ 
    if(j<m) nj[j] <-sum(as.numeric(X >= dh[j]& X < hh[j]))
    else nj[j] <-sum(as.numeric(X >= dh[j] & X <= hh[j]))}
  pj<-nj/n
  Nj<-cumsum(nj)
  Fj<-cumsum(pj)
 (Var.rada<-round(data.frame(dh=dh,hh=hh,stred=(dh+hh)/2,
                  nj=nj,pj=pj,Nj=Nj,Fj=Fj),digits=2))
}

(VR_pev<-VR(pevnost,dh_pev,hh_pev))

hist(pevnost,breaks=c(dh_pev,hh_pev[m]),col='khaki1',border='orange4',
     main='Pevnost oceli',xlab='pevnost',ylab='pocetnosti')

KT<-matrix(0,length(dh_pl),length(dh_pev))
for(i in 1:length(dh_pl)){
  for(j in 1:length(dh_pev)){
    KT[i,j]<-sum(as.numeric((plasticita>=dh_pl[i]& plasticita <hh_pl[i]) & 
                    (pevnost>=dh_pev[j]& pevnost < hh_pev[j])))}}
KT
round(KT/n,digits=2)
round(prop.table(KT,1),2)
round(prop.table(KT,2),2)
#=========================================================================================
library(lsr)
data<-matrix(c(13,15,14,11,7,2,19,9,10),3,3,byrow=T)
cramersV(data)
#===========================================================
data<-read.delim('znamky.txt',sep='',dec='.')
math<-data$math
english<-data$english
#math
quantile(math,0.5)
quantile(math,0.25)
quantile(math,0.75)
quantile(math,0.75)-quantile(math,0.25)

quantile(english,0.5)
quantile(english,0.25)
quantile(english,0.75)
quantile(english,0.75)-quantile(english,0.25)

boxplot(math,english,horizontal=F,main='Boxplot - znamky',
        range=1,asp=T,ylim=c(0,5),ylab='znamka',col='darkolivegreen1',border='darkgreen',type='n',
        xlab='predmet',names=c('math','english'))

Kor.koef<-cor(math,english,method='spearman')

pohlavi<-data$sex
(Kor.koef<-cor(math,english,method='spearman'))
(Kor.koef.zeny<-cor(math[pohlavi==0],english[pohlavi==0],method='spearman'))
(Kor.koef.muzi<-cor(math[pohlavi==1],english[pohlavi==1],method='spearman'))

#-----------------------------------------------------------------------
data<-read.delim('ocel.txt',sep='',dec='.')
head(data)
plasticita<-data$mez_plasticity
pevnost<-data$mez_pevnosti
n<-length(plasticita)
(prum_pl<-mean(plasticita))
(prum_pev<-mean(pevnost))
(sd_pl<-sd(plasticita))
(sd_pev<-sd(pevnost))
(rozptyl_pl<-sd_pl^2)
(rozptyl_pev<-sd_pev^2)

(koef.var_pl<-sd_pl/prum_pl)
(koef.var_pev<-sd_pev/prum_pev)
(sikmost_pl<-skewness(plasticita))
(sikmost_pev<-skewness(pevnost))
(spicatost_pl<-mean((plasticita-prum_pl)^4)/sd_pl^4-3)
(spicatost_pev<-1/n*(sum((pevnost-prum_pev)^4))/sd_pev^4-3)

cor(plasticita,pevnost,method='pearson')
cov(plasticita,pevnost,method='pearson')
X<-cbind(plasticita,pevnost)
cov(X)