FISHERY BULLETIN: VOL. 73, NO. 4 



I 



5:: 



10. 



1.:: 



0.1 



O01;; 



0.001 





^ 



o 





H — I I I I I II 



-I — I I II III 



0.1 



10. 100. 



DRY WEIGHT (mg/m^) 



lOOO 



k. 



k. 



1. T 



0.1 :: 



O01 :: 



0001 



H — I I I I I II 



H 1 — I I I I I II 



1. 10. 



DRY WEIGHT (mq/rrr>) 



100. 



10. T 



0.01 0.1 1. 



WET WEIGHT (g/m^) 



10. 



Figure 4. -Plots of data used in calculating geometric 

 mean regression lines relating wet weight and 

 displacement volume to dry weight and displacement 

 volume to wet weight. For symbols, see Table 1. 



Confidence limits can he calculated for predicted 

 values of Xor Y. Following Ricker (1973:411), the 

 general form of the variance estimate for a single 

 estimate of Y' given X' is: 



'yx 



f 



'\2 



-^ SSX' 



)■ 



(6) 



where S^v^ is the variance of observations from 

 the regression line in the vertical direction, A'^ is 

 the number of observation pairs in the regression, 

 and Pj.' is the value of X' used to estimate Y'. In the 

 reverse case where X' is being predicted, S^.y^, 

 SSY', Py., and Y' are substituted for Sy/ ,SSX\Py, 



and X'. Because we have used GM regression 

 equations rather than predictive regression equa- 

 tions, the use of Expression (6) is not strictly legi- 

 timate. However, Ricker (1973:413) finds the error 

 involved is small and concludes that "... it is pos- 

 sible to recommend using ordinary symmetrical 

 confidence limits for the GM regression. They are 

 a reasonable approximation to the true limits and 

 will rarely lead to incorrect conclusions." 



The values required to use Expression (6) to cal- 

 culate confidence limits for predicted A''s or Y's are 

 given in Table 3. This variance and the ^95 value are 

 used to construct confidence limits for the 

 logarithms: 



782 



