oto- 
fied 
ter. 
to- 
e of 
m 
1 . 
re the 
    
   
  
  
    
   
   
  
  
  
  
  
   
  
    
   
    
B 
© 
  
  
Part of the study area at the foot of Mt. Kulal with circles indica- 
ting some of the trees used in correlating ground and photo measure- 
ments of crown diameter. 
Fig. 1. 
The problem now requires that the covariance terms and V(Q) and V(R) be 
expressed in terms of the regression coefficients and their variances. 
ing to Mood et al (1974, p 180), 
Accord- 
V(Q) =V(bd) =dV(b) +bV(d) +V(b) V(d) 5. 
let S = be 
Then V(R) =V(SP) =PV(S) +SV(P) *V(S) V(P) 
and V(S) =eV(b) *bV(e) *V(b) V(e) 
so that V(R)=(eV(b) +bV(e) *V(b) V(e) ) P*beV(P) 
+(eV(b) +bV(e) +V(b) V(e) ) V(P) 
=eV(b)P+bPV(e) +PV(b) V(e) *beV(P) 
*eV(b) V(P) *bV(e) V(P) *V(b) V(e) V(P) 6. 
The calculations assume that COV(b,d),COV(b,e),COV(b,P),COV(d,P) and 
COV(e,P) are sero since the members of each pair were derived from inde- 
pendently measured data. 
2 2. 2 
Then COV(a,Q)=dCOV(a,b)=d(-C Sg/€ C- (EO) 7. 
n 
and — COV(a,R)=ePCOV(a,b)=eP(-C S/GC-E9)) 8. 
n 
2 2 
ad COV(Q,R)=b PCOV(d,e)-b P(-PS/(P-CP))) 9. 
+ N 
417 
  
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