#Načítanie dát
Yt <- c(6.1, 7.3, 9.6, 10.2, 10.1, 11.3, 12.2, 12.5, 13.2)
Pt <- c(103, 102, 100, 94, 98, 97, 98, 97, 96)
It <- c(110, 114, 130, 135, 141, 152, 160, 165, 170)

#Výpočet vektora parametrov b cez funkciu lm()
regresia = lm(Yt ~ cbind(Pt,It))

#VYPIS
regresia

#PODROBNEJSI VYPIS
summary(regresia)


#Výpočet vektora parametrov b cez vlastnú funkciu
#vlastná funkcia prináša aj grafické zobrazenie
reg = function (Yt, m)
{
  regr = lm (Yt~m)
  nr = nrow(m)
  nc = ncol(m)
  y = c()
  b = c()   
  for (i in 1:(nc+1))
  {
    b[i]=regr$coef[i]
  }    
  for (i in 1:nr)
  {
    ypom = 0;
    for (j in 2:(nc+1))
    {
      ypom = ypom + b[j]*m[i,(j-1)]
    }
    y[i]=b[1]+ypom
  }
  plot (Yt, type = "o", col="green",xlab="cas t",ylab="hodnoty y",
        main = "Linearna regresia")
  lines (y, type = "o", col="red")
  cat("Linear regresion","\n",
      "--------------------------------------","\n",
      "Estimated values of Y:","\n","\n",
      " ",y,"\n",
      "--------------------------------------","\n",
      "Summary from lm function:","\n"
  )
  summary (regr)
}

#volanie funkcie
reg(Yt,cbind (Pt,It))

#Výpočet vektora parametrov b cez matice
pom = rep(1,9)
X<-matrix(c(pom,Pt,It),9,3)
X = array( c(pom,Pt,It) , c(9,3) )
X
Xtran = t(X)
XXinv = solve(Xtran %*% X)
b = XXinv %*% Xtran %*% Yt
#výpis výsledkov
b