With this model, fraction cull will have an asymptotic maximum value of h and, there- 

 fore, should be less than or equal to 1. Unfortunately, this model does not prevent 

 fraction cull from becoming less than 0. 



The following process was used to determine the appropriate sp-NF parameters for 

 model (27). First, the model: 



Ind.O - 1^) = V (28) 



where 



FC = Actual fraction cull in total stem cubic foot volume given the tree is unsound 

 Y = A function of the tree's attributes 

 h = An intermediate constant value 



was screened through linear regression using various functions of d.b.h., total tree 

 height, number of tips, position to first fork, and damage information as independent 

 variables in Y, and also using various dependent variables formed by varying the value 

 of h from the maximum FC in the data set to a value of 1. For each combination group 

 with a specified number of independent variables from the screening run, that combina- 

 tion of Y and h which minimized RMSQR was picked, along with several other combinations, 

 that were almost as good. These models were next fitted, transformed back into model 

 (27), and then tabulated and checked for reasonableness. The model with the lowest 

 RMSQR that gave reasonable results was then fitted with least squares regression through 

 the origin for a slope correction to adjust the model for possible log bias. This slope 

 correction was then incorporated into the initial value of h to give the final value of 



in model (27). Y^ is the final function of Y. As a final check, the models were 

 again tabulated. 



On the Douglas-fir data set, the final model proved to be worse than a mean value 

 of FC,. Therefore, the following model was fitted: 



FC^ = bo - bie^. ' (29) 



The resulting model was better than the mean, and tabulation revealed that it behaved 

 correctly. Model (29) was easily transformed back to model (27) by setting Z^q equal to 

 7?^ and adding lr\{b\/bQ) to Y^. 



Again, data sets were combined based on the results of the screening runs and upon 

 the mean FC, values of the data sets to be combined. 



XII. Fraction Cull in Mercriantable Cubic Foot Volume Given the Tree Is Unsound — Unforked 

 and Forked Trees 



For each sp-NF combination, the same independent variables used in the total stem 

 cubic foot fraction cull models were fitted to each top diameter data set with a vari- 

 able h in model (28). An examination of the various runs across top diameter was made 

 and a value of h was picked that did the best overall job of minimizing the RMSQR 

 values . 



41 



