Regression of the Kill at Ages 3 and 4 on 

 Mean Air Temperature 



Table 30 shows the basic data for this re- 

 gression. The temperature regression is: 



Y = 17.61+0.98T (r^ = 0.59, r = 0.77) 



where: T is the mean air temperature in tenths 

 of a degree above 32°. 



Unfortunately, the highly significant relation 

 found several years ago between the annual 

 mean air temperature for the 12 months ending 

 30 June of the year of birth of the year class 

 and year-class returns continues to deterio- 

 rate. The validity of this relation has always 

 been dubious because the casual mechanism 

 is unclear. The estimated values of Y as de- 

 termined from the regression equation are in 

 table 31 for year classes 1957-64. 



Table 31. — Comparison of estimated and actual kill of 3- and 4- 

 year-old male seals, year classes 1957-64, St. Paul Island 



Year 

 class 



;^,¥f' 



Actual kill of 



3- and 4-year-old 



male seals 



Difference 



Although the average error for 1957-64 is 

 about 2.7 thousand, fluctuations have been 

 wide. Thus, this forecast method must be 

 evaluated carefully in the future. Setting 

 aside these reservations, the forecast for 

 the 1965 year class is found by setting T = 12. 



The kill at age 3 and 4 in 1965 was 29.4 

 thousand. Because the kill of 3-year-olds in 

 1968 was 18.7 thousand (plus some fraction of 

 the postseason kill), this method yields a re- 

 maining estimated balance of about 1 thousand. 

 The standard error is 9.7 thousand. 



Regression of the Kill at Ages 3 and 4 on the 

 Mean Weight of Living Seal Pups and the 

 Count of Dead Seal Pups 



The count of dead pups provided a forecast 

 that was too high, and the regression on mean 



weight of living pups provided one that was too 

 low. It seemed appropriate, therefore, to 

 consider a multiple regression using both 

 variables. Because pups were first weighed 

 in 1957, that year was used as a starting point. 

 The data for the regression are in table 30. 

 The resulting multiple regression equation is 



K = -12.14-0.25D + 6.73W (R^ = 0.56); 

 K, D, and W are defined in table 30. 



None of the F ratios shown in table 32 in an 

 analysis of the two variables are significant; 

 the variable D (count of dead pups) in par- 

 ticular seems to have little estimation value. 

 The forecast procedure is retained, however, 

 because its standard error is large and will 

 receive little weight. The total kill in 1968 of 

 the 1965 year class was estimated to be 41.5 

 thousand. The balance to be taken at age 4 is 

 about 22.0 thousand. The standard error of this 

 estimate is 9.3 thousand. 



-Analysis of variance in a regression of the total 

 kill of 3- and 4-year-old male seals (K) on count 

 of dead seal pups (D) and mean weight of living 

 seal pups (W) 



Sums of 

 squares 



Degrees of 

 freedom 



Mean 

 square 



F 

 ratio 



Due to regression of 

 K on D and W 



Due to regression of 

 K on D alone 



Due to regression of 

 K on W alone 



238.61 



104. 90 

 376. 15 



238. 61 3. 17 



104.90 1.39 

 75.23 



Estimate of the Kill Based on an Estimate of 

 the Yearling Male Seal Population 



Table 33 shows the estimates of the yearling 

 population surviving from the 1961, 1962, and 

 1964 year classes on the basis of recoveries 



Table 33. --Estimated number of yearling male seals, and the ratio 

 of the kill at ages 3 and 4 on St. Paul Island to the number of 

 yearling male seals, year classes 1961, 1962, and 1964 



1/ Based on recoveries at age 3; estimates from recoveries at 

 age 2 have been biased. 



25 



