Table 1 1 . — Analysis of improvement of ln(foliage weight)^ regression models attainable by varying parameters by species, trees 

 less than 3.5 inches d.b.h. 



Model= 



Source 



Remarks 



Degrees Marginal 



of sum of Mean square 

 freedom squares reduction 



(1) bo + bMCL) + bz\n{A) + baHTPA) 



(2) bg + bMCL) + bslniA) + b^TPA) 



(3) bo^ + bi^ln(CL) + bz\r\{A) + b^TPA) 



(4) bo, + bMCL) + b^ln(4) + bMTPA) 



(5) + bMCL) + bMA) + baMTPA) 



(6) bo, + bjjn{CL) + bj\n{A) + bMTPA) 



(7) bg + b^ln(CL) + b2ln(^) + b^^HTPA) 



(8) bo, + bMCL) + b2\n(A) + b^ln{rP/^) 



complete model 

 boj + biJn(CL) +b2^ln(4) + b^ln(rP/4) 



Reduction due 

 to model (1) 

 Reduction due 

 to model (2) 

 -reduction due 

 to model (1 ) 

 Reduction due 

 to model (3) 

 -reduction due 

 to model (2) 

 Reduction due 

 to model (4) 

 -reduction due 

 to model (2) 

 Reduction due 

 to model (5) 

 -reduction due 

 to model (2) 

 Reduction due 

 to model (6) 

 -reduction due 

 to model (3) 

 Reduction due 

 to model (7) 

 -reduction due 

 to model (3) 

 Reduction due 

 to model (8) 

 -reduction due 

 to model (4) 



Error 



inconsistent 

 signs in A term 



inconsistent signs 

 In TPA terms 



3 259.86645 86.62215 413.06 



10 32.33326 3.23326 15.42 



10 



inconsistent 



signs in A term 10 



inconsistent 



signs in TPA term 1 



10 



10 



inconsistent signs 



in /4 and terms 10 



inconsistent signs 



in /A and terms 166 



5.37841 .53784 2.56 



6.87378 .68738 3.28 



5.20996 .52100 2.48 



5.54004 .55400 2.64 



5.38501 .53850 2.57 



3.79663 .37966 1.81 



34.81201 .20971 



'Meanln(lVT) = - 0.075104 lb; standard deviation = 1.27874. 



^erms varying by species are underlined. 



^Tabulated F values: Fjgsoos = 1-89; P,?6,ooi = 2.43. 



Mean square error for the above model is 0.23751 , and 

 coefficient values are shown in table 1 2. Table 1 summarizes 

 the residuals for the model. Foliage weight is underestimated by 

 an average of 3.7 lb (1.7 kg) per tree. Negative bias may be 

 compensated for by multiplying the estimate in the natural scale 

 gi2,2375ii = 1 .126, giving an overprediction of 1 .1 lb (0.5 kg) 

 per tree after adjustment. 



The present approach for estimating foliage biomass uses 

 two model forms; one for small trees and one for large trees — 

 each of which is applicable to all species. The data used in 

 developing these equations were a subset of Brown's (1978) 

 data. His approach was to fit one or more separate model forms 

 for total crown biomass (foliage and branchwood) for trees 



greater than 1 inch d.b.h. and for trees less than 2 inches d.b.h., 

 by species and crown class. He further fitted separate regres- 

 sion equations for predicting the proportion of total crown 

 biomass in foliage and branchwood components. Foliage 

 weight can be estimated indirectly using Brown's method by 

 applying these two equations in succession to the data. The 

 following method was used to compare the present approach 

 with Brown's approach for predicting foliage biomass. The best 

 combination (that yielding lowest mean square error) of Brown's 

 crown biomass and foliage proportion equations for a species 

 was solved for each tree in the data set used to develop the 

 current equations. Residual sums of squares [^(observed - 

 predicted needle weight)^] were then compared for the two 

 methods. Results are as follows: 



10 



