EQUATION 1

Non-linear Regression

Notes
Output Created 19-OCT-2004 09:21:51
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\BreastHeightDiameter-Stump\d_d0.3.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 1050
Syntax MODEL PROGRAM b1=1 .
COMPUTE PRED_ = dhi / (1 + (b1 * var1)).
NLR D
/PRED PRED_.
Resources Elapsed Time 0:00:01,20

All the derivatives will be calculated numerically.





 Iteration  Residual SS          B1

     1      1,197486531  1,00000000
     1.1    17,04175207  -,35548393
     1.2    ,9893514013  ,864451607
     2      ,9893514013  ,864451607
     2.1    ,6120751972  ,629128557
     3      ,6120751972  ,629128557
     3.1    ,1223047238  ,276175451
     4      ,1223047238  ,276175451
     4.1    ,0812663988  ,179448578
     5      ,0812663988  ,179448578
     5.1    ,0810533161  ,185081382
     6      ,0810533161  ,185081382
     6.1    ,0810529888  ,185305013
     7      ,0810529888  ,185305013
     7.1    ,0810529884  ,185312446

Run stopped after 15 model evaluations and 7 derivative evaluations.
Iterations have been stopped because the relative reduction between successive
residual sums of squares is at most SSCON = 1,000E-08


Nonlinear Regression Summary Statistics     Dependent Variable D

  Source                 DF  Sum of Squares  Mean Square

  Regression              1       10,96215       10,96215
  Residual             1049         ,08105   7,726691E-05
  Uncorrected Total    1050       11,04320

  (Corrected Total)    1049         ,47950

  R squared = 1 - Residual SS / Corrected SS =     ,83096

                                           Asymptotic 95 %
                          Asymptotic     Confidence Interval
  Parameter   Estimate    Std. Error     Lower         Upper

  B1          ,185312446   ,003494070   ,178456284   ,192168607


EQUATION 2

Non-linear Regression

Notes
Output Created 19-OCT-2004 09:21:52
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\BreastHeightDiameter-Stump\d_d0.3.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 1050
Syntax MODEL PROGRAM b1=1 .
COMPUTE PRED_1 = dhi + (b1 * dhi * var2).
NLR D
/PRED PRED_1.
Resources Elapsed Time 0:00:00,40

All the derivatives will be calculated numerically.





 Iteration  Residual SS          B1

     1      7,145704604  1,00000000
     1.1    ,0630192069  -,29444095
     2      ,0630192069  -,29444095
     2.1    ,0630192069  -,29444095

Run stopped after 4 model evaluations and 2 derivative evaluations.
Iterations have been stopped because the relative reduction between successive
residual sums of squares is at most SSCON = 1,000E-08


Nonlinear Regression Summary Statistics     Dependent Variable D

  Source                 DF  Sum of Squares  Mean Square

  Regression              1       10,98018       10,98018
  Residual             1049         ,06302   6,007551E-05
  Uncorrected Total    1050       11,04320

  (Corrected Total)    1049         ,47950

  R squared = 1 - Residual SS / Corrected SS =     ,86857

                                           Asymptotic 95 %
                          Asymptotic     Confidence Interval
  Parameter   Estimate    Std. Error     Lower         Upper

  B1         -,294440952   ,003769919  -,301838393  -,287043512


EQUATION 3

Non-linear Regression

Notes
Output Created 19-OCT-2004 09:21:53
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\BreastHeightDiameter-Stump\d_d0.3.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 1050
Syntax MODEL PROGRAM b1=1 b2=1 .
COMPUTE PRED_2 = dhi + (b1 * dhi * (var2**B2)).
NLR D
/PRED PRED_2.
Resources Elapsed Time 0:00:00,76

All the derivatives will be calculated numerically.





 Iteration  Residual SS          B1          B2

     1      7,145704604  1,00000000  1,00000000
     1.1    ,0807640155  -,24573004  1,12721377
     2      ,0807640155  -,24573004  1,12721377
     2.1    ,0615048189  -,24081975  ,386422533
     3      ,0615048189  -,24081975  ,386422533
     3.1    ,0583121951  -,25019159  ,585622788
     4      ,0583121951  -,25019159  ,585622788
     4.1    ,0582975489  -,25154795  ,603814384
     5      ,0582975489  -,25154795  ,603814384
     5.1    ,0582975486  -,25155843  ,603918084

Run stopped after 10 model evaluations and 5 derivative evaluations.
Iterations have been stopped because the relative reduction between successive
residual sums of squares is at most SSCON = 1,000E-08


Nonlinear Regression Summary Statistics     Dependent Variable D

  Source                 DF  Sum of Squares  Mean Square

  Regression              2       10,98490        5,49245
  Residual             1048         ,05830   5,562743E-05
  Uncorrected Total    1050       11,04320

  (Corrected Total)    1049         ,47950

  R squared = 1 - Residual SS / Corrected SS =     ,87842

                                           Asymptotic 95 %
                          Asymptotic     Confidence Interval
  Parameter   Estimate    Std. Error     Lower         Upper

  B1         -,251558426   ,005447487  -,262247650  -,240869203
  B2          ,603918084   ,039913591   ,525598430   ,682237737

  Asymptotic Correlation Matrix of the Parameter Estimates

                  B1        B2

  B1          1,0000    -,8249
  B2          -,8249    1,0000


EQUATION 4

Non-linear Regression

Notes
Output Created 19-OCT-2004 09:21:53
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\BreastHeightDiameter-Stump\d_d0.3.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 1050
Syntax MODEL PROGRAM b1=1 b2=1 .
COMPUTE PRED_3 = dhi + (b1 * ((dhi * var2)**B2)).
NLR D
/PRED PRED_3.
Resources Elapsed Time 0:00:01,01

All the derivatives will be calculated numerically.





 Iteration  Residual SS          B1          B2

     1      7,145704604  1,00000000  1,00000000
     1.1    ,1232279333  -,37933466  ,964291248
     2      ,1232279333  -,37933466  ,964291248
     2.1    ,0633180807  -,36828418  1,07253085
     3      ,0633180807  -,36828418  1,07253085
     3.1    ,0621077848  -,39802581  1,12798000
     4      ,0621077848  -,39802581  1,12798000
     4.1    ,0621014552  -,40767486  1,13764002
     5      ,0621014552  -,40767486  1,13764002
     5.1    ,0621013565  -,40883781  1,13873989
     6      ,0621013565  -,40883781  1,13873989
     6.1    ,0621013556  -,40895941  1,13886547
     7      ,0621013556  -,40895941  1,13886547
     7.1    ,0621013556  -,40897313  1,13887982

Run stopped after 14 model evaluations and 7 derivative evaluations.
Iterations have been stopped because the relative reduction between successive
residual sums of squares is at most SSCON = 1,000E-08


Nonlinear Regression Summary Statistics     Dependent Variable D

  Source                 DF  Sum of Squares  Mean Square

  Regression              2       10,98110        5,49055
  Residual             1048         ,06210   5,925702E-05
  Uncorrected Total    1050       11,04320

  (Corrected Total)    1049         ,47950

  R squared = 1 - Residual SS / Corrected SS =     ,87049

                                           Asymptotic 95 %
                          Asymptotic     Confidence Interval
  Parameter   Estimate    Std. Error     Lower         Upper

  B1         -,408973133   ,032809475  -,473352875  -,344593391
  B2         1,138879817   ,033898183  1,072363779  1,205395856

  Asymptotic Correlation Matrix of the Parameter Estimates

                  B1        B2

  B1          1,0000    -,9874
  B2          -,9874    1,0000


EQUATION 5

Non-linear Regression

Notes
Output Created 19-OCT-2004 09:21:54
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\BreastHeightDiameter-Stump\d_d0.3.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 1050
Syntax MODEL PROGRAM b1=1 b2=1 .
COMPUTE PRED_4 = dhi + (b1 * dhi * var3).
NLR D
/PRED PRED_4.
Resources Elapsed Time 0:00:00,30

All the derivatives will be calculated numerically.





 Iteration  Residual SS          B1          B2

     1      ,8591711831  1,00000000  1,00000000
     1.1    ,0686335008  ,403205239  1,00000000
     2      ,0686335008  ,403205239  1,00000000

Run stopped after 3 model evaluations and 2 derivative evaluations.
Iterations have been stopped because the magnitude of the largest correlation
between the residuals and any derivative column is at most RCON = 1,000E-08


Nonlinear Regression Summary Statistics     Dependent Variable D

  Source                 DF  Sum of Squares  Mean Square

  Regression              2       10,97456        5,48728
  Residual             1048         ,06863   6,548998E-05
  Uncorrected Total    1050       11,04320

  (Corrected Total)    1049         ,47950

  R squared = 1 - Residual SS / Corrected SS =     ,85686

                                           Asymptotic 95 %
                          Asymptotic     Confidence Interval
  Parameter   Estimate    Std. Error     Lower         Upper

  B1          ,403205239   ,005431892   ,392546617   ,413863862
  B2         1,000000000   ,000000000  1,000000000  1,000000000

  Asymptotic Correlation Matrix of the Parameter Estimates

                  B1        B2

  B1          1,0000     ,
  B2           ,        1,0000


EQUATION 6

Non-linear Regression

Notes
Output Created 19-OCT-2004 09:21:55
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\BreastHeightDiameter-Stump\d_d0.3.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 1050
Syntax MODEL PROGRAM b1=1 b2=1 b3=1 .
COMPUTE PRED_5 = dhi + (b1 * dhi * var2) + (b2 * (dhi**2) * var2) + (b3 * (dhi**2) * var2).
NLR D
/PRED PRED_5.
Resources Elapsed Time 0:00:00,91

All the derivatives will be calculated numerically.





 Iteration  Residual SS          B1          B2          B3

     1      10,61297012  1,00000000  1,00000000  1,00000000
     1.1    ,0515618667  -,09608495  495,877706  -497,28839
     2      ,0515618667  -,09608495  495,877706  -497,28839
     2.1    ,0515618666  -,09608112  1489,10688  -1490,5176
     3      ,0515618666  -,09608112  1489,10688  -1490,5176
     3.1    ,0515618667  -,09607874  1985,72146  -1987,1322
     3.2    ,0515618666  -,09607897  1737,40284  -1738,8136
     3.3    ,0515618666  -,09607909  1613,24806  -1614,6588
     3.4    ,0515618666  -,09607914  1551,17247  -1552,5832
     3.5    ,0515618666  -,09607917  1520,13549  -1521,5462
     3.6    ,0515618666  -,09607919  1504,61735  -1506,0281
     3.7    ,0515618666  -,09607919  1496,85846  -1498,2692

Run stopped after 12 model evaluations and 3 derivative evaluations.
Iterations have been stopped because the relative reduction between successive
residual sums of squares is at most SSCON = 1,000E-08


Nonlinear Regression Summary Statistics     Dependent Variable D

  Source                 DF  Sum of Squares  Mean Square

  Regression              3       10,99164        3,66388
  Residual             1047         ,05156   4,924725E-05
  Uncorrected Total    1050       11,04320

  (Corrected Total)    1049         ,47950

  R squared = 1 - Residual SS / Corrected SS =     ,89247

                                           Asymptotic 95 %
                          Asymptotic     Confidence Interval
  Parameter   Estimate    Std. Error     Lower         Upper

  B1         -,096081118   ,013668226  -,122901353  -,069260883
  B2        1489,1068751 2678832,5207 -5255002,702 5257980,9155
  B3        -1490,517581 2678832,5441 -5257982,372 5255001,3370

  Asymptotic Correlation Matrix of the Parameter Estimates

                  B1        B2        B3

  B1          1,0000     ,1799    -,1799
  B2           ,1799    1,0000   -1,0000
  B3          -,1799   -1,0000    1,0000


EQUATION 7

Non-linear Regression

Notes
Output Created 19-OCT-2004 09:21:56
Comments
Input Data C:\Documents and Settings\kiki\Desktop\Rennolls\BreastHeightDiameter-Stump\d_d0.3.sav
Filter <none>
Weight <none>
Split File <none>
N of Rows in Working Data File 1050
Syntax MODEL PROGRAM b1=1 b2=1 .
COMPUTE PRED_6 = b1 * (dhi**b2).
NLR D
/PRED PRED_6.
Resources Elapsed Time 0:00:00,86

All the derivatives will be calculated numerically.





 Iteration  Residual SS          B1          B2

     1      ,4294820000  1,00000000  1,00000000
     1.1    ,8575858643  ,401810753  ,776758386
     1.2    ,1499172704  ,777658645  ,955984474
     2      ,1499172704  ,777658645  ,955984474
     2.1    ,1822383451  ,500964886  ,777162627
     2.2    ,1306415880  ,692162583  ,894691267
     3      ,1306415880  ,692162583  ,894691267
     3.1    ,1249253822  ,528020256  ,778483615
     4      ,1249253822  ,528020256  ,778483615
     4.1    ,1123198793  ,499156675  ,736629584
     5      ,1123198793  ,499156675  ,736629584
     5.1    ,1123093075  ,500761093  ,737705838
     6      ,1123093075  ,500761093  ,737705838
     6.1    ,1123093073  ,500767891  ,737710059

Run stopped after 14 model evaluations and 6 derivative evaluations.
Iterations have been stopped because the relative reduction between successive
residual sums of squares is at most SSCON = 1,000E-08


Nonlinear Regression Summary Statistics     Dependent Variable D

  Source                 DF  Sum of Squares  Mean Square

  Regression              2       10,93089        5,46544
  Residual             1048         ,11231   1,071654E-04
  Uncorrected Total    1050       11,04320

  (Corrected Total)    1049         ,47950

  R squared = 1 - Residual SS / Corrected SS =     ,76578

                                           Asymptotic 95 %
                          Asymptotic     Confidence Interval
  Parameter   Estimate    Std. Error     Lower         Upper

  B1          ,500767891   ,012901985   ,475451227   ,526084555
  B2          ,737710059   ,012125223   ,713917580   ,761502538

  Asymptotic Correlation Matrix of the Parameter Estimates

                  B1        B2

  B1          1,0000     ,9926
  B2           ,9926    1,0000