## Exercises

1. 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)$using the default parameters. What is the predicted$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 $f(168)$.

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