/* Create Data for problem 3 from chapter 6 */
capture clear
input byte y  byte x
 1 1
 2 1
 3 1
 1 2
 2 2
 3 2
 1 3
 2 3
 3 3
20 20
end
list, noobs


/* Problem 3a */
pwcorr y x, sig


/* Problem 3c */
quietly {
  sum x
  local sx=r(sd)
  reg y x
  local n=e(N)
  local sse=e(rss)
  local syx=(`sse'/(`n'-2))^.5
  local t1=_b[x]/(`syx'/(`sx'*((`n'-1)^.5)))
  corr y x
  local r=r(rho)
  local t2=(`r'*((`n'-2)^.5))/((1-`r'^2)^.5)

  noisily di _n _col(2) "Method 1: t-test for r= " %5.2f `t1'
  noisily di    _col(2) "Method 2: t-test for r= " %5.2f `t2'
}


/* Problem 3d */
quietly {
  #delimit ;
  graph twoway (scatter y x, 
                  msymbol(circle)       /* Change shape of markers     */
                  msize(large)          /* Make markers larger         */
                  mlwidth(medium)       /* Change marker outline width */
                  mlcolor(maroon)       /* Change marker outline color */
                  mfcolor(ebblue))      /* Change marker fill color    */
               (lfit    y x, lw(thick))
  ;
  # delimit cr
}