# slr1.r
 # first probe on SimStudy problem 2
 # normality of L1 regression
 #
  y <- c(4.5,5.5,6.5,8,10,12)
  x <- (1:6)
 #
  g <- function(b) {
         res <- y - b*x
         med <- median(res)
         g <- sum(abs(res-med)) }
 # 
 # simple linear regression
  slr <- function(y,x) {
    xb <- mean(x)
    yb <- mean(y)
    sxx <- sum((x-xb)*(x-xb))
    b1 <- sum((x-xb)*(y-yb))/sxx
    b0 <- yb - b1*xb
    sse <- sum((y-b0-b1*x)*(y-b0-b1*x))
    slr <- c(b1,sqrt(sse/((length(x)-2)*sxx)))   }
 #
    rslt <- slr(y,x)
    rslt
    int <- c(rslt[1]-4*rslt[2],rslt[1]+4*rslt[2]) # +/- 4 se's
    int
 # use optimize on smoother function 
    this <- optimize(g,int)
    this
 # done
  rm(list=ls())
 q()