This was transformed back by taking the antilog of both sides and a least squares slope 

 correction was made on the resulting model to correct it for possible log bias. Tabu- 

 lation of this model showed that it did behave reasonably. 



VIII. Gross Saribner Board Foot Volume — Un forked Trees 



As described by Avery (1967) , the ratio of Scribner board foot volume divided by 

 International board foot volume starts well below 1.0 at small diameters and then 

 increases monotonically toward an asymptotic value of 1 as diameter increases. This 

 relationship can be expressed as 



Rg^j = ao - aiD"^ - azD"^ (19) 



where 



Rg,j = Predicted ratio of actual gross Scribner board foot volume to a 6- inch top 

 divided by predicted gross International 1/4-inch board foot volume to a 

 6-inch top. 



The signs on and a2 must be positive and ag must be near 1 for the model to behave 

 reasonably. 



Individual values of Rg/j were formed and plotted across d.b.h. for all sp-NF 

 combinations used in gross cubic foot equation development. All data below 9 inches — 

 d.b.h. and certain outliers were eliminated based on the results of the plots. This 

 was necessary because the ratio values below 9 inches started to turn upward and exceed 

 1 as d.b.h. decreased. This problem was attributed to the way in which Scribner volume 

 is estimated in program NETVSL. The elimination of trees under 9 inches should not 

 cause problems because Scribner volume is seldom computed for trees under that limit. 



Equation (19) was fitted to the corrected data set. Weights were developed using 

 the basic model: 



Vg = X (Rg^j) X (Vj) ^ e (20) 



where 



Vg = Predicted gross Scribner board foot volume to a 6-inch top 

 hi = Least squares regression coefficient 

 c = Residual about regression 



and the same process as described for International 1/4-inch board foot volume. An 

 examination of the final weighted least squares regression coefficients, after the slope 

 correction was multiplied through the ratio model, revealed that only the models for 

 yellow pine, both blackjack pines, and white fir on the Santa Fe and Carson National For- 

 ests were reasonable. 



An abbreviated ratio model: 



h/i = ^0 - ^1^'^ (21) 



was then tried using the same weighted scheme as previously described. This model 

 proved reasonable for Engelmann spruce-corkbark fir, aspen, and Douglas-fir on the Santa 

 Fe and Carson National Forests. 



38 



