Body Length and Scale Length in Pacific Pilchard — Landa 
173 
TABLE 4 
Regression Values Found for Homogeneous Groups 
GROUPS 
N* 
by.xt 
Sxt 
Sy§ 
r|| 
Sy.xl 
Sb ** 
y.x 
Y.tt 
x.« 
a§§ 
(Y)llll 
(X)1I1[ 
1938 year-class 
237 
15.90 
.58 
14.42 
.64 
11.1 
1.24 
210 
5.20 
127 
202 
124 
1939 year-class 
483 
21.90 
.70 
19.89 
.77 
12.7 
.85 
211 
5.17 
98 
204 
154 
1940 year-class in; 
Pacific Northwest. 
14 
57.00 
.17 
22.43 
.43 
20.3 
32.54 
226 
5.76 
-102 
222 
164 
San Francisco 
50 
11.66 
.54 
13.14 
.479 
11.5 
3.01 
227 
5.65 
161 
228 
170 
Monterey 
75 
20.45 
.73 
22.23 
.67 
16.4 
2.60 
213 
5.30 
105 
200 
152 
San Pedro 
70 
21.38 
.55 
14.56 
.81 
8.5 
1.86 
201 
5.00 
94 
204 
152 
1941 year-class in: 
San Francisco 
5 
5.00 
.55 
10.00 
.28 
9.6 
8.10 
220 
5.80 
191 
222 
170 
Monterey 
26 
25.36 
.57 
20.28 
.71 
14.3 
4.99 
210 
5.40 
73 
200 
152 
San Pedro 
90 
16.64 
.42 
10.94 
.64 
8.4 
2.10 
199 
5.06 
115 
196 
146 
1942 year-class in: 
Pacific Northwest. 
7 
28.00 
.72 
24.20 
.83 
13.5 
7.63 
233 
5.63 
75 
216 
164 
San Francisco 
23 
10.50 
.58 
16.62 
.37 
15.4 
5.65 
217 
5.53 
159 
216 
164 
Monterey 
68 
25.40 
.73 
22.89 
.81 
13.3 
2.20 
200 
5.13 
70 
186 
140 
San Pedro 
51 
26.20 
.60 
18.94 
.83 
10.5 
2.35 
202 
5.10 
68 
202 
152 
* N = number of items in the group. 
NSX'Y'-(2X0(2Y0 
t hy.x = regression coefficients of y on x = NSX'^— (SX')^ 
[For actual calculation the uncoded values were used: X' = (X') 
30X; Y' 
{ Sx = Standard deviation of mean scale length = 
V 
'2X'2(2X')2 
N 
N-1 
§ Sy = Standard deviation of mean body length 
^x 
II r = correlation coefficient =-^ — by.x 
y 
1 Sy.x = Standard error of estimate = Sy(l— r) 
1 
2 
/2Y'2(SY')2 
/ N 
^ N-1 
(Y)-Y] 
** Sb = variance of regression coefficient = - 
SxVn-1 
2Y' 
ft Y. = mean body length = + assumed mean of Y 
N 
SX^ 
X. = mean scale length = h assumed mean of X 
N 
§§ a = body intercept = Y. — bX. 
III! (Y) = assumed mean of Y 
Ifl (X) = assumed mean of X 
30 
deviate significantly from a straight line 
(Tests 1 to 6 and Table 4). 
(4) The values found for the y-intercepts 
are so great that it seems likely that the 
regressions do not pass through the 
origin (0.0) although this was not 
tested. 
These answers imply that, in order to back- 
calculate lengths, the formula ln = a+bsn (in 
which In = body length at age n and sn = scale 
length at age n) should be used in which, for 
each homogeneous group, the values of ”a” 
and "b” are different (see Table 4). These 
values are used in a separate work for a study 
of the rate of deceleration of growth in the 
Pacific sardine. It should be noted that the 
formula given above, which applies to aver- 
ages, suits our purpose quite well as long as 
