Table 5. — Summary of residuals (natural scale) from prediction equations for 

 crown width of trees. Bias adjustment factors are 1.025 for trees 

 greater than or equal to 3.5 inches d.b.h., and 1 .031 for trees less than 

 3.5 inches 



Trees sS.S inches d.b.h . Trees <3.5 inches d.b.h . 



X (obs-pred) (obs-pred) 



No. of without with bias No. of without with bias 



Species^ trees correction correction trees correction correction 



BP 



7 



- 0.71 



-1.93 



12 



0.61 



-0.19 



WP 



8 



1.59 



- .36 



17 



- .03 



-2.12 



WC 



25 



-1.25 



-11.26 



25 



1.70 



-2.00 



WL 



9 



- .03 



-3.08 



15 



1.25 



- .27 



WH 



12 



.15 



-5.66 



16 



2.08 



.20 



AF 



10 



- .80 



-3.00 



15 



.58 



-1.01 



LP 



7 



5.68 



3.73 



12 



.29 



- .08 



GF 



22 



1.80 



-6.09 



29 



1.55 



-2.40 



ES 



8 



2.35 



- .43 



14 



.52 



- .98 



DF 



23 



9.95 



2.07 



28 



4.19 



.78 



PP 



29 



21.02 



10,30 



27 



8.84 



5.66 



Weighted mean 













residual (Mree) 



5.67 



-1.18 





2.48 



-0.07 





(m/tree) 



(1.73) 



(-0.36) 





(0.76) 



(-0.02) 



'See text page 2 for species list. 



The general model for prediction of crown width for 21 trees 

 less than 3.5 inches (8.9 cm) d.b.h. is: 



\n(CW) = biln(H) + b2ln(CL) + b3ln(e>4) 



In this model for smaller trees the density effect, as measured 

 by the basal area term, is positive rather than negative as might 

 be expected (table 6). One possible explanation is that there is 

 no competition effect among small trees due to stocking. In- 

 stead, the density effect is positive in that small trees in a 

 well-stocked stand expand laterally to utilize all available space. 

 As the stand matures with time, closure of the canopy begins, 

 and individual tree crowns start to compete, stocking may nega- 

 tively affect crown width. This argument would assume that the 

 measured stands are mainly even-aged, and would not hold for 

 suppressed trees with weak crowns. That more than three- 

 fourths of the data are from dominant or codominant trees helps 

 support this explanation. 



Table 6. — Coefficients for estimating 



ln(crown width) of trees less than 3.5 inches: 

 In(ClV) = bi, ln(H) + b2ln(CL) -i- b3ln(S4) 



Species^ 



Variable coefficients 

 ln(H) 



BP 



0.07049 



WP 



.37031 



WC 



.46452 



WL 



.23846 



WH 



.25622 



AF 



.33722 



LP 



.26342 



GF 



.38503 



ES 



.33089 



DF 



.32874 



PP 



.36380 



Variables 



Variable coefficients 



In(CL) 



ba = .28283 



\n{BA) 



bg = .04032 



Regression sum of squares/d.f. 

 Error sum of squares/d.f. 

 Mean square error 



= 371.02441/13 

 = 11.89093/197 

 = 0,06036 

 = 0,9689 



'See text page 2 for species list. 



6 



