Accordingly, the inverse of the geometric mean is given by: 



= exp[Z ln(fl )/n] 



[/' CAfl)] 2 



The index-of-fit is 3.54 for the best collection of variables (through level 4) in the 

 finite difference model. This index is compared to the standard error of estimate of 

 the differential model, which is ±2.93 feet. Hence, the differential model is superior. 



Table 3 is an analysis of variance for the finite difference model with comparisons 

 similar to those in table 2. The variables in this model that are analogous to those in 

 the differential model are effective as predictors to about the same degree. 



Table 3. --Analysis of improvement of regression model attributable to adding variables. 



Dependent variable = ln(ff 2 /#i) 



Comparison 

 level 



Source 



d.f. 



Proportion of 

 remaining variance 

 explained!/ 



Marginal 

 sum of squares!/ 



Mean 

 square 



In {D 2 /D^ 



3. 1589 



3. 1589 



1707.5 



[ ln(Z> 2 /0O ] 9 



0.091 



3372 



0375 



20.3 



.031 



. 1365 



0152 



8.2 



3 



1 . 9 



.015 



.0754 



.00838 



4 



5 





[ ln(ff) ] 1 



.252 



.7702 



.7702 



416 



3 



4 



[ HJ)/D, (AD/D) 2 ] 2 



.258 



.5921 



.2961 



160 







5 



1 . 9 



.018 



.04633 



.00515 



2 



8 





Error 886 







.00185 









- Increase m explanatory power 



for regression due to adding 



variables to 



the 





model 



composed of those variables bracketed in 



Differential Model 



the levels above. 



Logarithmic Form 









When the differences between the observed and predicted values of A# are plotted 

 over the predicted values, the variance of the difference increases with larger values 

 of the prediction. As a consequence, faster growing trees are given undue weight in 

 estimating values of the coefficients. The logarithmic form of the model (3) should 

 decrease the variance of the residuals associated with large predictions. The pre- 

 ceding analyses showed that the allometric coefficient (b) varied with species and the 



11 



