2017-11-02 untitled from rstudio

untitled-2017-11-02.R

library(plyr)
library(MASS)

test <- raply(50000, {
  dat <- mvrnorm(200, mu = c(0,1), Sigma = matrix(c(1,.3,.3,1), nrow=2))
  y <- dat[,1]
  x <- dat[,2]
  
  # throw away most of the data, introduce huge bias
  y <- y[x > 1]
  x <- x[x > 1]
  
  lm_fit <- lm(y~x)
  mu <- mean(y)
  lmu <- coef(lm_fit)[1] + coef(lm_fit)[2]
  
  c(mu, lmu)
}, .progress="text")

mus <- test[,1]
lmus <- test[,2]

# There is really a striking improvement by using the correlation
mean((mus)^2)
mean((lmus)^2)

# corrected model not too bad on average
colMeans(test)