To compare whether the alternative model approximates the 

 fit obtained by the general model, both models were applied to 

 an independent stand data set^ in which both periodic and mean 

 annual increments were measured. The tree ages in this stand 

 ranged from 2 to 560 years. For 95 trees in the test data set. the 

 chi-square value for the sum of squared differences between 

 needle weight prediction by the alternative model and prediction 

 by the general model was 4. 1 compared to the tabulated value 

 of 95. 005 = 134.24. The alternative model overpredicts 

 needle weight outside of the range of data used to develop the 

 general model (the sum of differences between predictions by 

 the alternative and current models was 741 .3 lb [336.2 kg] for 

 the 95 trees). However, with the low chi-square value, the 

 alternative model may be judged adequate, and also uses 

 independent variables that are more readily available. 



For trees less than 3.5 inches (8.9 cm) d.b.h., the following 

 reparametenzed alternative model substituting height for age is 

 presented: 



\n(WT) = bo, + biln(H) + b2ln(CL) + b3HTPA) 



Mean square error is 0.24759 for the coefficients given in table 

 13. This model underestimates needle weight for 9 of 1 1 spe- 

 cies (table 14). On the average, it underpredicts needle weight 

 by 3.6 lb (1 .6 kg). A correction for underestimation of e' " = 

 1 .1 32 may be applied giving a mean overprediction of 1 .0 lb (0.5 

 kg) after bias adjustment. Residual sum of squares obtained for 

 this alternative equation is 46.0511, which is also lower than 

 that obtained from Brown's method. Thus, the alternative 

 formulation is judged acceptable. 



Table 13.— Coefficients for estimating In (foliage weight) of trees 

 less than 3.5 inches d.b.h., alternative model: 

 In(lVT) = bo, + biln(H) -t- b^ln(CL) + b3ln(7P4) 



Species^ 



Variable coefficients 



Intercept 



bo, 



In(CL) 



BP 





1 .35092 



Wr 



- 1 .94951 



1 .22023 



WC 



-2.24876 



1 .37600 



WL 



-4.73762 



1 .98479 



WH 



-4.17456 



2,00749 



AF 



-1.60998 



1 .32649 



LP 



-3.13488 



1.62368 



GF 



-2.43200 



1 ,60270 



ES 



-2.93508 



1.96125 



DF 



-2.05828 



1 .25837 



PP 



-2.74410 



1.58171 



Variables 



Variable coefficients 





ln(H) 



b, = .40350 





ln( TPA) 



b2 = - .12975 





Regression sum of squares d.f. 

 Error sum of squares/d.f. 

 Mean square error 



295.70288 23 

 46.05106 186 

 0.24759 

 0.8653 



'See text page 2 for species list. 



Table 14. — Summary of residuals (natural scale) from alternative 

 prediction equation for foliage weight of trees less than 

 3.5 inches d.b.h. The bias correction factor is 1.132 



!i (obs — pred) 



No. of without with bias 



Species^ trees bias correction correction 



BP 



12 



1.41 



0.11 



WP 



17 



1.85 



-1.74 



WC 



25 



5.74 



.74 



WL 



15 



-.45 



-2.15 



WH 



16 



1.14 



-3.00 



AF 



5 



5.83 



.87 



LP 



12 



-.09 



-1.32 



GF 



29 



3.44 



-5.29 



ES 



14 



1.63 



-2.85 



DF 



28 



7.39 



1.46 



PP 



27 



5.23 



1.36 



Weighted mean residual 



(lb tree) 3.62 - 1 .03 



(kg tree) (1.64) (-.47) 



'Seetextpage 2 for species list 



"St. Joe National Forest. Idaho. 



13 



