## Demonstrate how the correlation between coefficient estimates is
## related to the correlation of the covariate data.

nrep = 1e3

## The correlation between the covariates.
r = 0.4

n = 30

B = array(0, c(nrep,3))

## How this is specified should not matter.
beta = c(0,1,-1)

for (k in 1:nrep) {

  ## Generate the design matrix.
  X1 = rnorm(n)
  X2 = r*X1 + sqrt(1-r^2)*rnorm(n)
  X = cbind(array(1, n), X1, X2)

  ## Generate the outcome.
  Y = X %*% beta + rnorm(n)

  ## Fit the model and store the coefficients.
  m = lm(Y ~ X+0)
  B[k,] = m$coefficients
}