Details of Methodology 



J. Total Stem Gross Cubic Foot Volume — Unforked Trees 



The basic model of 



V = ao + aiD2H 



(1) 



where 



V = Predicted total stem gross cubic foot volume in an unforked tree 



D = D.b.h. in inches 



H = Total tree height in feet 



has been used for years for predicting total stem gross cubic foot volume (Husch 1963) . 

 Weighting this model by- 



was suggested by Cunia (1964) as a me_^ans for homogenizing the variance about regression. 

 This model and weighting procedure was applied to each sp-NF combination and a plot of 

 residuals indicated that the variance was homogenized by the weighting. However, 

 Pearson's beta statistics computed for each equation indicated that the residuals were 

 not normally distributed. This problem precluded the usage of this model for testing 

 the possibility of combining species across National Forests or of combining some of 

 the species with others, using analysis of covariance. 



It was then hypothesized that the following mocal might eliminate the problem: 



The plots of residuals again confirmed that variance was homogenized and Pearson's beta 

 statistics this time indicated that the residuals were closer to being normally distri- 

 buted. Analysis of covariance was then applied to see if species could be combined 

 across forests. The results indicated that blackjack pine, Douglas-fir, and white fir 

 on the Santa Fe and Carson National Forests could not be combined with the same species 

 on the other National Forests. All other species were combined across Forests. 



Only two "species" combinations were tested. One was whether yellow pine and 

 blackjack pine could be combined. Results of the testing indicated that they could not 

 be combined, a conclusion supported by the findings of Hornibrook (1936) and Myers 

 (1963) . The other combination tested was Engelmann spruce with corkbark fir. This 

 test was made because of the small data set for corkbark fir. This test resulted in 

 the combining of Engelmann spruce with corkbark fir. 



These final data sets were fitted to equation (1) using weighted least squares 

 regression. For aspen, this resulted in a negative intercept. Therefore, an intercept 

 value of 0.0327 (the volume of a tree 2 inches in diameter at the root collar and 4.5 

 feet tall, assuming conical shape) was forced on the equation instead of forcing it 

 through the origin. 



All final equations were visually checked by plotting the predicted and actual 

 volumes over diameter by height classes. 



W = (0%) 



-2 



(2) 



In(V^) = ao + ailn(H) + a2ln(D). 



(3) 



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