1. Generate the following data:

     n = 10000
     men = rnorm(n,176,7) #height in centimeters
     women = rnorm(n,162,7) #height in centimeters
     y = c(rep(0,n),rep(1,n))
     x = round(c(men,women))
     ##mix it up
     ind = sample(seq(along=y))
     y = y[ind]
     x = x[ind]

    Set the seed at 5, set.seed(5) and take a random sample of 250 from:

     N = 250
     ind = sample(length(y),N)
     Y = y[ind]
     X = x[ind]
    Use loess to estimate $$f(x)=E(Y X=x)f(168)$?
  2. The loess estimate above is a random variable. We can compute standard errors for it. Here we use Monte Carlo to demonstrate that it is a random variable. Use Monte Carlo simulation to estimate the standard error of your estimate of .

    Set the seed to 5, set.seed(5) and perform 10000 simulations and report the SE of the loess based estimate.