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  A^A^*- 
  

  

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  ^ 
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  A 
  

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  AA 
  

  

  3.5 
  14.5 
  5.5 
  6.5 
  7.5 
  

  

  UK 
  OF 
  DffiQtL 
  

  

  Figure 
  3.— 
  Log 
  transformation 
  of 
  volume 
  

   plotted 
  against 
  DRSQH 
  for 
  Utah 
  juniper 
  trees 
  

   from 
  the 
  Moab 
  BLM 
  District. 
  

  

  8.5 
  

  

  9.5 
  

  

  C 
  

   U 
  

   B 
  

   E 
  

  

  R 
  

   

   

   T 
  

  

  a 
  

  

  F 
  

  

  C 
  

   U 
  

   B 
  

   I 
  

   C 
  

  

  F 
  

   

   

   T 
  

  

  V 
  

   

   L 
  

   U 
  

   M 
  

   E 
  

  

  U.OH 
  

  

  3.5- 
  

  

  3.0- 
  

  

  2.5- 
  

  

  2.0- 
  

  

  1.5- 
  

  

  1.0 
  

  

  0.5- 
  

  

  0.0- 
  

  

  A 
  

  

  A 
  

  

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  A 
  A 
  

  

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  '!«1A 
  AA 
  

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  A^ 
  

  

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  AAA 
  

   A 
  

  

  n 
  A 
  A. 
  

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  ^ 
  A 
  

  

  2.5 
  7.5 
  12.5 
  17,5 
  

  

  CUBE 
  FtCOT 
  OF 
  DRSQH 
  

  

  Figure 
  4. 
  — 
  Cube 
  root 
  transformation 
  of 
  vol- 
  

   ume 
  plotted 
  against 
  DRSQH 
  for 
  Utah 
  juniper 
  

   trees 
  from 
  the 
  Moab 
  BLIvl 
  District. 
  

  

  Rather 
  than 
  discard 
  data 
  or 
  conduct 
  a 
  multiagency 
  edit, 
  

   I 
  used 
  a 
  weighted 
  regression 
  method 
  to 
  minimize 
  the 
  

   effect 
  of 
  those 
  data 
  points 
  that 
  fell 
  far 
  from 
  the 
  regres- 
  

   sion 
  line. 
  The 
  observations 
  were 
  weighted 
  in 
  regression 
  

   by 
  the 
  following 
  biweight 
  function 
  (MosteUer 
  and 
  Tukey 
  

   1977): 
  

  

  (1-u^) 
  

  

  U; 
  

  

  < 
  1 
  

  

  0, 
  

  

  -V,.)/6M 
  

  

  elsewhere 
  

  

  with 
  

   where 
  

  

  W; 
  = 
  biweight 
  of 
  the 
  ith 
  tree 
  

  

  = 
  visually 
  estimated 
  volume 
  of 
  the 
  ith 
  tree 
  

   = 
  predicted 
  volume 
  from 
  the 
  regression 
  of 
  the 
  ith 
  

  

  (2) 
  

  

  tree 
  

  

  M 
  = 
  the 
  median 
  of 
  all 
  (Vj— 
  quantities 
  (that 
  is, 
  the 
  

   median 
  residual 
  from 
  a 
  regression). 
  

  

  Figure 
  5 
  illustrates 
  the 
  effects 
  of 
  biweight 
  function 
  on 
  

   the 
  residuals 
  for 
  Utah 
  juniper 
  from 
  the 
  Ely 
  BLM 
  Dis- 
  

   trict. 
  The 
  outlying 
  data 
  points 
  are 
  clearly 
  minimized 
  in 
  

   this 
  figure. 
  However, 
  the 
  effect 
  of 
  the 
  biweight 
  function 
  

   on 
  parameter 
  estimation 
  was 
  less 
  dramatic. 
  For 
  example, 
  

   the 
  parameter 
  estimates 
  (in 
  eq. 
  1) 
  for 
  the 
  Ely 
  data 
  were 
  

   a 
  = 
  -0.036033, 
  b 
  = 
  0.135638, 
  and 
  c 
  = 
  -0.018677 
  be- 
  

   fore 
  biweighting 
  and 
  a 
  = 
  -0.036549, 
  b 
  = 
  0.135689, 
  and 
  

   c 
  = 
  -0.018476 
  after 
  biweighting. 
  

  

  10.0'+ 
  

  

  7.5 
  + 
  

  

  5.0 
  + 
  

  

  66 
  

  

  2.5 
  + 
  

  

  1 
  3 
  

   6 
  

   4 
  778888 
  

  

  8 
  88 
  8 
  

   9 
  99 
  99 
  99 
  

  

  99 
  9 
  

  

  99 
  

  

  8898999 
  99 
  9 
  9 
  9 
  99 
  9 
  

  

  0.0 
  +-99899999999-9999-9—9-9-9-9-9 
  

  

  9999689899 
  999 
  99 
  9 
  9 
  

   5 
  8 
  88 
  8 
  89 
  

  

  68 
  77 
  8 
  

   6 
  7 
  7 
  

   -2.5 
  + 
  

  

  -5.0 
  + 
  

  

  9 
  9 
  

  

  1 
  2 
  3 
  4 
  5 
  6 
  7 
  

  

  CUBIC 
  FOOT 
  PREDICTED 
  VOLUME 
  

  

  Figure 
  5. 
  — 
  A 
  residual 
  plot 
  from 
  a 
  biweight 
  

   regression 
  of 
  Utah 
  juniper 
  from 
  the 
  Ely 
  BLM 
  

   District. 
  The 
  numbers 
  represent 
  the 
  percent 
  

   of 
  each 
  observation 
  used 
  in 
  the 
  bivi/eight 
  

   regression: 
  0=0 
  to 
  4 
  percent, 
  1=5 
  to 
  14 
  per- 
  

   cent. 
  ..9=85 
  to 
  100 
  percent. 
  

  

  4 
  

  

  