/*************************************************
 *  Kleinbaum, Chapter 6, Problem #1, p. 104     *
 *************************************************/

/* Read in the data */
capture clear
input age weight
 6 0.029
 7 0.052
 8 0.079
 9 0.125
10 0.181
11 0.261
12 0.425
13 0.738
14 1.130
15 1.882
16 2.812
end


/* Create log base 10 variable */
generate logweight=log10(weight)
format weight %9.3f
format logweight %9.3f
list

/* Chapter 6, problem 1a, p. 104 */
pwcorr age weight logweight, sig 

di _n(2) "Chapter 6, problem 1b, p. 104: 95% Confidence Intervals"
z_r age weight logweight, level(95)  /* User written r confidence interval p-rogram */

quietly {
  corr age weight
  local alpha=0.05
  local z=invnormal(1-(`alpha'/2))
  local se=(r(N)-1)^.5
  local rz=.5*(ln((1+`r(rho)')/(1-`r(rho)')))
  local lb=`rz' - (`z'/`se')
  local ub=`rz' + (`z'/`se')

  local lb1 = (exp(2*`lb')-1)/(exp(2*`lb')+1)
  local ub1 = (exp(2*`ub')-1)/(exp(2*`ub')+1)
  #delimit ;
  noisily di _n _col(2) "r= "  %4.3f r(rho) _col(12) 
                        "LB= " %4.3f `lb1'  _col(23) 
                        "UB= " %4.3f `ub1'  _col(34)
                        "n= "  r(N);
 #delimit cr

  corr age logweight
  local alpha=0.05
  local z=invnormal(1-(`alpha'/2))
  local se=(r(N)-1)^.5
  local rz=.5*(ln((1+`r(rho)')/(1-`r(rho)')))
  local lb=`rz' - (`z'/`se')
  local ub=`rz' + (`z'/`se')

  local lb1 = (exp(2*`lb')-1)/(exp(2*`lb')+1)
  local ub1 = (exp(2*`ub')-1)/(exp(2*`ub')+1)
  #delimit ;
  noisily di    _col(2) "r= "  %4.3f r(rho) _col(12) 
                        "LB= " %4.3f `lb1' _col(23) 
                        "UB= " %4.3f `ub1'  _col(34)
                        "n= "  r(N);
 #delimit cr
}


/* Chapter 6, problem 1c, p. 104 */
quietly {
  regress age weight
  local numer1=e(mss)
  local denom1=((e(mss)+e(rss)))
  noisily di "age regressed on weight:    r2= " %6.4f `numer1'/`denom1'

  regress age logweight
  local numer2=e(mss)
  local denom2=((e(mss)+e(rss)))
  noisily di "age regressed on logweight: r2= " %6.4f `numer2'/`denom2'
}