Generate the following data:
n = 10000 set.seed(1) 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:
set.seed(5) 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)$?
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.