#Seeks to find a design of 10 values of x to minimise the variance of beta0-hat
#for a standard straight-line regression.  The points must all lie between 0 and 1
#
nsimulations <- 10000
n <- 10
set.seed(1234)
minv <- 100
for (i in 1:nsimulations)
{
 xvec <- runif(n)
 sumx <- sum(xvec)
 sumxsq <- sum(xvec^2)
 v <- sumxsq/(n*sumxsq - sumx^2)
 if (v < minv) {minv <- v
                bestx <- xvec}
}
cat("minimum V =",minv,"\n")
cat("best set of x-values = ","\n",bestx,"\n")