x<-c(2,3,4,5,6)
y<-c(4,4,6,6,10)
x;y

(n<-length(x))

(sumx<-sum(x))
(sumy<-sum(y))
(mx=mean(x))
(my=mean(y))
(xy<-x*y)
(sumxy<-sum(xy))
(sumxsq<-sum(x^2))
(sumysq<-sum(y^2))

beta1<-(sumxy-mx*sumy)/(sumxsq-mx*sumx)
beta0<-my-beta1*mx
beta0;beta1

(b1hat<-cov(x,y)/var(x))
(b0hat<-mean(y)-b1hat*mean(x))

X<-matrix(c(1,1,1,1,1,2,3,4,5,6), nrow=5, ncol=2)
Y<-matrix(c(4,4,6,6,10), nrow=5)
N<-length(Y)

X
(XPX<-t(X)%*%X)
(XPXINV<-solve(XPX))
(XPY<-t(X)%*%Y)
(beta<-XPXINV%*%XPY)

ols<-lm(y~x)
summary(ols)