TV. Merohantable Gross Cubic Foot Volume — Forked Trees 



To maintain consistency across top diameters, the same model used in predicting 

 total stem gross cubic foot volume was fitted to each top diameter data set. The 

 resulting regression coefficients were examined for trends over top diameter. From this 

 examination, the regression coefficients were modeled as linear functions of top diam- 

 eter. The basic model with the coefficients as functions of top diameter was then 

 fitted to the whole data set for a final overall slope correction on the model. Models 

 with forking variables that proved not to be better than models without forking vari- 

 ables were dropped. 



Because the RMSQR values of the models were high, it was decided to provide an 

 optional model that would predict the mean ratio as a function of just top diameter. 

 To do this, the mean ratio values for the six top diameters were weighted by their 

 respective number of observations and then screened against 12 power transformations 

 on top diameter. Selected models were then examined for reasonableness of behavior and 

 the one that behaved both reasonably and minimized RMSQR was picked as the final model. 



V. Gross Cubic Foot Stump Volume — Un forked and Forked Trees 

 The basic model: 



V^^ = ao + aiD2 (11) 



where 



V = Gross volume of the stump in cubic feet 



S L' 



was fitted to the separate sp-NF combinations. The residuals were plotted and they 

 revealed that the basic model was appropriate but that the variance increased with the 

 square of D^. Therefore, the model was refitted using a weight of 



W = D"''. (12) 



The residuals were plotted and this time they were homogeneous. 



Analysis of covariance was then used to determine if species could be combined 

 across all National Forests except the Lincoln, where stump height was 1.2 feet instead 

 of the standard of 1.0 foot. The results indicated that they could be so combined. 

 Analysis of covariance was also used to check to see if Engelmann spruce and corkbark 

 fir could still be legitimately combined, and the results indicated that they could. 



VI. Gross International 1/4-Inch Board Foot Volume — Unforked Trees 



The approach of modeling the ratio of gross International 1/4-inch board foot 

 volume to a 6-inch top divided by the gross merchantable cubic foot volume to a 6-inch 

 top was used to provide the needed control on the behavior of the International 1/4-inc 

 model. It has long been recognized that this ratio starts with a zero value at a d.b.h 

 near 6 inches and increases monotonically, as d.b.h. increases, to an asymptotic ratio 

 value between 6 and 8 (Husch 1963; Avery 1967). It has also been shown that this ratio 

 can be affected by tree height as well (Husch 1963). 



35 



