round of the kill of 3-year-old males seals; 

 (2) regression of returns at ages 3 and 4 on 

 mean air temperature; and (3) regression of 

 returns at ages 3 and 4 on estimated number 

 of yearlings. 



Regression of the Kill of 4-year-old Male 

 Seals on the Kill of 3-year-old Male Seals and 

 the Mean Round of the Kill of 3-year-old 

 Male Seals 



A regression was originally substituted for 

 the estimate of the kill of 4-year-old males 

 based on the estimated escapement of 3-year- 

 olds. One problem with this regression has 

 been variations in the terminal date of the kill 

 of 3-year-old males; many of the data had to 

 be "adjusted" accordingly. In the past, this 

 regression has been based on the kill to 

 31 July, the approximate terminal date in the 

 early l950's. In 1965, however, the mean 

 round^ of the kill of 3-year-old male seals fell 

 outside the range observed in past years. 

 Associated with this deviation was a forecast 

 that seemed unreasonable (the actual kill has 

 since proved that the forecasted kill of 25,000 

 4-year-old males was much too high). Foruse 

 in forecasting the kill of 4-year-old males in 

 1967, we have modified the method by using 

 only the data for the 195 3 and later year 

 classes and for the kill through 5 August each 

 year. This change has minimized the need for 

 adjusting the data; in only 2 years since 1956 

 has the kill of males ended before 5 August. 

 Additionally, to make the mean round calcula- 

 tions consistent throughout the series, all kills 

 before the round of 7-11 July have been pooled 

 with the kill for this round. Thus, the data for 

 all years have been made closely comparable. 

 The data for this regression are shown in 

 table 22. 



The resulting regression is: 



Table 22. --Data for regression of the kill of 4-year-old male 

 seals on the kill of 3-year-old male seals and mean round o: 

 the kill of 3-year-old male seals, year classes 1953-62, 

 St. Paul Island 



? = -49,420 + 0.38Xi + 14,540X2 



(1) 



For the 1963year class: X^^ = 25,500X2 = 3.7 

 and hence Y = 14,100. 



The standard error of the forecast, Y, is 

 1,800. 



The coefficient of multiple correlation of Y 

 with Xi, X2 is 0.96 (R^ = 0.92), indicative of a 

 very strong relation. 



Because of this very high correlation, there 

 can be no practical gain in making additional 

 regressions based on similar data; however, 

 we explored the possibility of replacing the 

 mean round with the median date of the kill of 

 3 -year-old males. The median date is also 

 unaffected by variations in the beginning date 

 of the kill, if we can safely assume that seals 

 arriving before this date are taken early in 



1/ The mean round of the kill of 3-year-old males through 5 

 August; kills before 7 July were pooled into the round of 7-11 

 July and this period was considered as round 1. 



2/ The kill of 4-year-old males before 5 August adjusted ac- 

 coTding to termination of the kill of 3-year-old males the previ- 

 ous year. If killing ended after 5 August, this figure was in- 

 creased by 80 percent of the number of 3-year-old nnales taken 

 after 5 August. If killing ended 5 August, this figure was de- 

 creased by 80 percent of the estimated nunnber of 3-year-old 

 males that could have been taken from the actual termination date 

 through 5 August. 



3/ The killing of males in 1958 ended 31 July; an estimated 

 4, "000 3-year-old males could have been taken 1-5 August. 



4/ The killing of males in 1959 ended 31 July; an estimated 

 1. 500 3-year-old males could have been taken 1-5 August. 



the season. If the median date rather than the 

 mean round for X2 is used, then R = 0.93 

 {r2 = 0.86). 



We also tried to forecast the kill of 4-year- 

 old males in 1966 by using the regression of 

 percentage of kill taken at age 3 on date of 

 termination and the mean date of the kill of 

 3-year-olds. For the 1966 data, the value of R 

 (the multiple coefficient of correlation) was 

 0.64, An additional year of data did not change 

 this value. The regression follows; 



p = 60. 3-2. 37m + 2.01t 



where p = percentage of the kill of 3- and 4- 

 ^ year-old males from a year 



class taken at age 3 

 m = median date in days after 20 July 

 t = termination date (in days after 

 31 July) 



The regression used to forecast the kill of 

 4-year-old males in 1966 was similar: 



p^ = 62. 4-2. 21m + 1.95t 



(2) 



^Mean round = mean of rounds weighted by number taken 

 by round. See glossary. 



The current regression yields a value of 66.1 

 for P3 for the 1963 year class, and a forecast 

 of a kill of 9,700 4-year-old males in 1967. 

 Though difficult to determine exactly, the 

 standard error of this forecast is about 5,000. 

 Since the forecast based on regression (1) has 



26 



