LAKE TROUT BREEDING HABITS 



63 



was the partial regression of the spawning date 

 statistically significant. When both factors were 

 considered in a multiple regression coefficient the 

 result was significant (7?=. 8643 when R of .836 

 or greater is to be expected 5 percent of the time 

 with 5 degrees of freedom). 



Table 2. — Reduced data for tnutliple regression analysis of 

 the date of peak of lake-trout egg take at Raquetle Lake 



i, = Avera!;e air temperature for the month of September 

 at Indian Lake. 



i2= Number of cloudy days in July, August, and Septem- 

 ber in the northern plateau region of New York. 



?/=Date of peak of lake-trout egg take. 



Number of observations: n = 8 



Means: 



i, = 54.81 X2 = 21.00 17=10.25 



Sums of squares: 



&,2= 16.01 



Sums of products; 

 Sj 1X2= -6.80 



Sx22 = 24.00 5i/2 = 65.50 



Sz2y= -27.00 St,!/ = 23.08 



Correlation coefficients: 



r,2=-.3469 r,2=-.6810 r„ = .7534 



Standard partial regre.ssion coefficients: 



B„,.2 = .5675 B„2.,= -.4841 



Multiple regression equation: 



B= - 80.3 -I- 2.32A',- 1.32X2 



Tests of Sionikic^nce: 



Standard partial regression coefficients: (DF = 5) 



.5675 



for B„i 2 ( 

 for B„2 1 ( = 



.2398 

 .4841 



= 2.366 

 = 2.019 



.2398 

 neither significant 

 Multiple correlation or multiple regression: (DF = b) 

 /? = .8643 significant 



A similar analysis of data on the peak of egg 

 take from Upper Saranac Lake (tables 3 and 4) 

 was less conclusive. The date of peak of egg take 

 in 1941 was about a month later than usual, but 

 if we omit this aberrant observation the date of 

 the peak at Upper Saranac Lake seems to bear 

 the same relation to air temperature and cloudiness 

 as at Raquette Lake. However, neither the partial 

 nor the multiple regression coefficients are signifi- 

 cant. (R=. .699 when R of .930 or greater is to be 



expected 5 percent of the time with 3 degrees 

 of freedom). 



Table 3. — Wealher conditions in relation to peak of lake-trout 

 egg take in Upper Saranac Lake, 1935-41 



I Average air temperature for tlie month of Septemljcr at nearby Tupper 

 Lake. 



' Number of cloudy days in July, .\ugust, and Septemi>er in the northern 

 plateau region of New York. 



Table 4. — Reduced data for the multiple regression anaylsis 

 of the date of the peak of lake-trout egg take at Upper 

 Saranac Lake 



ii = Average air temperature for the month of September 

 at Tupper Lake. 



i2 = Number of cloudy days in July, August, and Septem- 

 ber in the northern plateau region of New York. 



y=Date of peak of lake-trout egg take. 



Number of observations: n = 6 ' 



Means: 



*, = 53.87 



Sums of squares: 



Sxi2= 19.03 



Sums of products: 

 Si,X2= -28.10 



i2 = 22.00 j/ = 21.00 

 5x2' = 66.00 Si/2 = 90.00 

 Sx2)/=- 62.00 5x,!/= 19.00 



Correlation coefficients: 



r,2=-.7929 r,2=-.6263 r„, = .4591 



Standard partial regression coefficients: 



B„i.2=-1008 B„2.i=--7062 



Multiple regression equation: 



£:= 50.94 -.219A'i-.825A'2 



Tests op Significance: 



Standard partial regression coefficients: (Df = 3) 



.1008 



for B„i.2 < = 

 for /?„2 1 ' = 



6776 

 7062 



= .1488 



= 1.0421 



6776 



neither significant 



Multiple correlation or multiple regression: (,DF = S) 

 ff = .6990 not significant 



1941 data omitted. 



