#
# eisagwgn dedomevwv
#
x<-scan()
96 77 0 0 78 64 89 47 90 93 18 86 0 30 59 77 74 67


y<-scan()
95 80 0 0 79 77 72 66 98 90 0 95 35 50 72 55 75 66

cbind(y,x)
 
#
# pra3eis gia ta elaxnsta tetpagwva 
#
cbind(y,x,y*x,x*x)

cbind(sum(y),sum(x),sum(y*x),sum(x*x))

yx.lm<-lm(y~x)

yx.lm

#
# diagramma diasporas
#

plot(x,y,pch=21,col="blue",bg="red")

abline(yx.lm,col="red")

#
# problepomeves times kai ektimnseis twv sfalmatwv (kataloipa)
#

cbind(x,y,yx.lm$fitted.values,yx.lm$residuals)
sum(yx.lm$residuals)

yhat<-yx.lm$fitted.values

join <- function(i){
lines(c(x[i],x[i]),c(y[i],yhat[i]),col="green")}
sapply(1:10,join)

predict(yx.lm,list(x=c(45)))

#
# katallnlotnta modelou, avalusn diasporas, 
# R^2 (suvtelestns prosdiorismou)
#

summary(yx.lm) 

anova(yx.lm)