1.  Think of the body as consisting of chunks stacked on top of each
other.  A person's height is the sum of the heights of the chunks, so
the CLT suggests overall height is normal.

2.  

library(regtools)
data(mlb)
print(cor(mlb[,4:6]))

3.  

myLm <- function(inputMatrix,yColNum)
{ 
   x <- inputMatrix[,-yColNum]
   a <- cbind(1,x)
   apai <- solve(t(a) %*% a)
   apd <- t(a) %*% inputMatrix[,yColNum]
   apai %*% apd
}

pred <- function(betahat,newx)
{
   t(betahat) %*% c(1,newx)
}

library(regtools)
data(mlb)
mlb1 <- as.matrix(mlb[,4:6])
z <- myLm(mlb1,2)
print(z)
print(pred(z,c(70,21)))

4.  

load('Hwk1.RData')
library(qeML)
ml100 <- ml100[,-4]
# do our own holdout
set.seed(9999)  # so we are all on the same page
idxs <- sample(1:nrow(ml100),1000)
trn <- ml100[-idxs,]
tst <- ml100[idxs,]
mlout <- qeLin(trn,'V3',holdout=NULL)
preds <- predict(mlout,tst[,-3])
preds <- round(preds)
ratingValues <- as.numeric(names(table(ml100$V3)))
preds <- pmin(preds,max(ratingValues))
preds <- pmax(preds,min(ratingValues))
mean(preds == tst$V3)