#Fit the Least Squares Line to bivariate normal data.
#Start with Z_1, Z_2 iid standard normal.
#Construct X=Az
#where z = (z_1, z_2)' and A is 2x2 with independent standard normal entries.
#Cov(X)=AA' and this yields the correlation which is printed out.
#
n=50
A=0*diag(2)
A[1,1]=rnorm(1)
A[1,2]=rnorm(1)
A[2,1]=rnorm(1)
A[2,2]=rnorm(1)
#
xbig=NULL
for(iter in 1:n)
  xbig=cbind(xbig,A%*%rnorm(2))
covmat=A%*%t(A)
rho=covmat[1,2]/sqrt(covmat[1,1]*covmat[2,2])
plot(xbig[1,],xbig[2,],xlab="x",ylab="y")
title(main=paste("Simulated Data and Least Squares Line 
n=",n, ", Corr(X,Y)=",round(rho,2)))
abline(lsfit(xbig[1,],xbig[2,]))
#