1.  p-hacking

2.  

 map01 <- function(x) {
   m <- min(x); M <- max(x)
   newx <- (x - m) / (M - m)
   tmp <- list(m=m,M=M,newx=newx)
   class(tmp) <- 'm01'
}

newNile <- map01(Nile)  # Nile is a built-in dataset in R
print(sd(newNile$newx))  # about 0.185

3.  We will need to predict new cases in the future, and must transform 
them in the same way.  Hence we need to retain m and M.

4.  

lp <- function(x,p) {
    if (p == Inf) return(max(x))
    (sum(x^p))^(1/p)  
}

# LakeHuron is another built-in dataset
print(lp(LakeHuron,2))  # about 5731.9
print(lp(LakeHuron,1))  # 56742.4
print(lp(LakeHuron,Inf))  # 581.86

5.  We wish to do dimension reduction.  ZIP codes are arranged so that
the first two digits do give us some regional information, e.g. 94 for
all the Bay Area.