Height data were missing for some of Fahnestock's trees. To complete the data set, 

 height was estimated from height-d . b . h . relationships of trees from the same area. 

 Crown ratio was withheld from the screening process for dead crown weights. For screen- 

 ing, program RHX provides a printout that lists ratios of residual mean square to total 

 mean square for all possible combinations of variables. From the screening, several 

 variable combinations having small residual mean squares were selected and details of 

 multiple regression analysis examined using the following criteria to determine the best- 

 fitting equations. The equations should: 



1. Give unbiased predictions for the data collected; 



2. fit trees greater than approximately 4 inches d.b.h. reasonably well; 



3. give positive predictions throughout the range of independent variables; 



4. have as low a residual mean square as possible; and 



5. give reasonable extrapolations beyond the range of sample data. 



To determine whether site quality and stand density could improve prediction of 

 live crown weight beyond d.b.h., height, crown length, and crown ratio, variables from 

 the "best-fitting equations" were screened together with site index, trees per acre, and 

 basal area per acre. When regression coefficients for site and stand density variables 

 (from equations selected in screening) were significant at the 0.90 probability level, 

 they were considered influential. 



Trees having a d.b.h. less than 2 inches underwent a separate regression analysis, 

 with height as the only independent variable. For trees 4 inches and less, functions 

 for estimating total bole weight were determined in the same manner as for crown weights, 

 except only d.b.h. and height were involved in the screening process. 



Foliage J Branahwoodj and Bole Fractions 



For each tree, the fractions of dead branchwood by size class were computed assum- 

 ing that the proportion of weight in each size class for the dead sample branch repre- 

 sented the size distribution for all dead branches. However, for live crowns, fractions 

 of foliage and branchwood b^y size classes were determined in four steps involving all 

 branches on a tree: 



1. Simple linear regressions between weights of each crown component and branch 

 basal diameter were determined using sample branch data. Besides branches randomly 

 picked from each crown section, additional branches were collected to assure having 

 branches of large basal diameters. Natural log transforms of dependent and independent 

 variables were used and weights estimated from: 



s2 



(a + b(lnX) + ~) 



where 



y = ovendry weight of foliage or branchwood by size classes, lb 

 X = basal diameter of branch, inch 

 s^ - sample variance of the logarithmic equation used to correct for an approximate 



bias in converting logarithmic estimates to arithmetic units (Baskerville 



1972) . 



2. Solving equation (1) for tallies of branches by basal diameters, weights of 

 foliage and branchwood by the 0- to 0.24-inch, 0.25- to 0.99-inch, 1.00- to 2.99-inch, 

 and 3 . 00-inch-and-over classes were computed for the live crown sections of sample trees. 



7 



