The functional (GM) regressions for straight 

 fork length-round weight (log transformation), 

 round weight-dressed weight, and straight fork 

 length-curved fork length are presented in Table 

 1. All of these relationships were characterized by 

 high correlation coefficients. The data points are 

 plotted with regression lines in Figures 1-3. The 

 data points show that the GM regression model 

 fits the data reasonably well for the size ranges 

 studied. Extrapolation beyond the size range of 

 observations may yield erroneous predictions. Re- 

 gression statistics for each relationship are pre- 

 sented in Table 2. 



The use of logarithmic transformations may 

 lead to bias in data estimates (Pienaar and Thom- 

 son 1969; Beauchamp and Olson 1973; Lenarz 

 1974). However, since the mean square error for 

 the round weight-straight fork length logarithmic 

 transformation is low (Table 2), the bias in the 

 data estimate was found to be minimal ( 19c ). 



Previous publications have not included stan- 

 dard errors or confidence limits or statistics neces- 

 sary for their estimation. Therefore, comparisons 

 with my data could not be made. To compare re- 

 sults from my study with studies by other authors, 

 I compared estimates of Y using both their regres- 

 sion equations and mine. Whenever possible, I 



Table l. — Functional (GM1 regression equation and correlation 

 coefficient for the relationships between round weight (Y) and 

 straight forli length (X), round weight (Yl and dressed weight (X). 

 and straight fork length (Y) and curved fork length (X) for 

 western Atlantic bluefin tuna. Weights in kilograms and lengths 

 in centimeters. 



Geometric mean regression equation r 



Log,o round weight - 109,0 straight foric length 

 log,„y= -4 52307 + 2 91920 log, oJ< 

 Round weight - dressed weight 



Y = -7 92240 + 1 29607 X 

 Straight fork length - curved fork length: 



y = -2 06971 ^ 963300 X 



997 

 0.935 

 0,892 



selected X values at each end of their range of 

 values that corresponded with my range of values. 

 I also compared estimates of Y for an X value 

 taken at the middle of their size range. 



My estimates of round weight from straight fork 

 length using the functional (GM) regression 

 agreed most closely with my estimates obtained 

 using the regression equation of Sakagawa and 

 Coan (1974), with the greatest difference in esti- 

 mates of only 2% occurring for a 270 cm fork 

 length (FL) bluefin tuna. My calculated functional 

 regression estimates next most closely agreed 

 with estimates obtained using the length-weight 

 relationship of Butler ( 1971), with the largest dif- 

 ference of 6% occurring at 250 cm FL. My esti- 



o 



Figure l.— Functional (GM) regression of 

 round weight on straight fork length for 3,578 

 western Atlantic bluefin tuna 1974-77. 

 (Number of fish indicated, star signifies 

 number >9.) 



STRAIGHT FORK LENGTH (Cm) 



997 



