Table 8. 



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

 3.5 inches d.b.h. and larger 



Degrees Marginal 











of 



sum of 









Model^ 



Source 



Remarks 



freedom 



squares Mean square 





(1) 



bo + b,ln(D) + b2ln(/-/) + bglnlCL) 



Reduction due 

















to model (1 ) 





6 



152.41829 



25.40305 



126.59 





+ bi\r\{A) + bsiniTPA) + belniDREL) 



Residual from 

 model (1) 





107 



21.47126 



.20067 





(2) 



bo + biln(D) + b2ln(H) + bglnlCL) 



Reduction due 

















to model (2)-(1) 





9 



8.43661 



.93740 



7.05 





+ bi\n(A) + bglni rP/A) + beHDREL) 



Residual from 

 model (2) 





98 



13.03464 



.13301 





(31 



bo + biln(D) + bzlniH) + b3\n{CL) 



Reduction due 

















to models (3)-(2) 





9 



1 .35027 



.15003 



1.14 





+ b4ln(/4) + bs\r\{TPA) + beHDREL) 



Residual from 

 model (3) 





89 



11.68435 



.13128 





(4) 



bg + biln(D) + bgln(H) + baHCL.) 



Reduction 















to models (4)-{2) 





9 



1.60567 



.17841 



1.39 





+ b^HA) + bsHTPA) + beHDREL) 



Residual from 

 model (4) 





89 



1 1 .42897 



.12842 





(5) 



bg + b,ln(D) + b2ln(H) + b3_ln(Ci.) 



Reduction due 

















to model (5)-(2) 





9 



2.20900 



.24544 



2.02 





+ bMA) + br,\r\(TPA) + be\r\(DREL) 



Residual from 



inconsistent 















model (5) 



signs in CL terms 



89 



10.82565 



.12164 





(6) 



bo + b,ln(D) + b2ln(H) + b3ln{CL) 



Reduction due 

















to models (6)-(2) 





9 



.75875 



.08431 



.61 





+ b^\r\{A) + bsHTPA) + be\r\(DREL) 



Residual due 



inconsistent 















to model (6) 



signs in A term 



89 



12.27590 



.13793 





(7) 



b^ + b,ln(D) + b2ln(H) + bMCL) 



Reduction due 

















to models (7)-(2) 





9 



.81401 



.09446 



.66 





+ b4ln{/A) + bs^miTPA) + be\n(DREL) 



Residual from 



inconsistent 















model (7) 



signs in TPA term 



89 



12.22063 



.13731 





(8) 



bg + bJn(D) + b2ln(H) + b3\n{CL) 



Reduction due 

















to models (8)-(2) 





9 



1.41581 



.15731 



1.20 





-f b4ln(>^) + bs\n{TPA) + belniDREL) 



Residual from 



inconsistent 















model (8) 



signs in DREL terms 



89 



11.61885 



.13055 





'Meanin(VVT) = 3 41782 lb; standard deviation = 1.24050. 

 ^erms varying by species are underlined. 



by species, there was no significant species interaction with any 

 of the variables in the general model except for \n{CL). How- 

 ever, since the signs of the coefficients for the species x \r\{CL) 

 term were inconsistent, this model was rejected as possibly 

 overfitting the data. 



Thus, the final model is that in which just the intercept term 

 varies by species: 



In(ia'r) = bo, + biln(D) + b2ln(H) + b3in(CL) + 

 bMA) + bs\n(TPA) + be\n(DREL) 



The coefficients in table 9 gave a residual mean square of 

 0.1 3301 . Note that since there were no data available for lodge- 

 pole pine, no parameters were estimated for this species. Table 

 1 shows for which species the model overpredicts and under- 

 predicts. The mean prediction underestimates foliage biomass 

 by 86.9 lb (39.4 kg). A correction for bias of e' = 1 .069 may 

 be applied, resulting in an overprediction of 5.7 lb (2.6 kg) per 

 tree after adjustment. 



In the above model, predicted foliage weight decreases as 

 trees per acre increase, an indication of competitive stress due 

 to stocking. The positive crown length and negative height, 

 which reflect crown ratio in the natural scale, and positive rela- 

 tive diameter terms may all be interpreted as measures of an 

 individual tree's cbmpetitive status. In addition, the negative 

 age term coupled with the positive diameter term may be inter- 

 preted as an estimator of mean annual diameter increment in 

 the natural scale, which would be expected to vary directly with 

 foliage weight. As tree age is not always a readily available 

 measurement in inventory data, an alternative equation for 

 foliage weight involving a transformation of the diameter and 

 age terms is presented in a later section. 



8 



