In describing the length-weight relation, 

 I assumed that weight is an exponential func- 

 tion of length. This assumption was substan- 

 tiated by plotting samples of each set of data 

 on log-log paper. This relation, expressed 

 empirically as Y = aX", was used in the 

 logarithmic form, i.e., 



log, Y = log, a + b log 10 



X 



where 



Y = total weight in grams 



X = total length in millimeters 

 a and b are constants 



I assumed a linear relation of the form 

 Y = a + bX between total weight and tail 

 weight, where 



Y = total weight in decigrams 

 X = tail weight in decigrams 

 a and b are constants 



Landing statistics are given only in units of 

 tails per pound and tail weight; however, bi- 

 ologists frequently require information on 

 the total weight as well as the headless weight 

 of shrimp. Thus it is necessary to be able to 

 convert from headless to total weight and vice 

 versa. Because both regression equations, one 

 relating headless to whole weight and another 

 relating whole to headless weight of shrimp, 

 are equally important, both equations were 

 computed. 



A UNI VAC 1107 at the University of Ala- 

 bama performed the mathematical computa- 

 tions using an unpublished program made 

 available by the Bureau of Commercial Fish- 

 eries Biological Laboratory at Galveston, 

 Tex. 



RESULTS AND DISCUSSION 



The regression equations for estimating log 

 weight (Y) from log length (X) are listed by 

 sex and by area in table 2. The estimated 

 variances of the regression coefficients (b) 



Table 2. — Regression equations for estimating log weight (Y) from log length (X) of royal-red 

 shrimp. Estimated variances of the regression coefficient s£ are listed by sex and area; esti- 



are listed for 



mated standard errors of the difference between regression coefficients S 



each area. 



Values of t compare b,-, and b* 



for each area (weight in grams) ? 



V tw 



■^Significant at the 95 percent level. 



