where the symbols have the following values and meanings: [10.6] X_o: the log of the area of the group for which the population is being estimated. X_i: the log of the area of each of the groups for which the population is already known. [=X]: the average of the X_i. t_[oc]: the upper [oc]-point of the t-distribution (Bennett and Franklin, 1954, p. 696) where 1-[oc] is the confidence coefficient. _________________________________ {1 } S_a = [Sqrt]{- × =S=(Y_i + 4.06 - 1.02X_i)^2} {4 } where Y_i is the population of each of the groups for which population is known. This is the estimated standard deviation of population where the estimate is made from area. [Illustration: Fig. 2. Simple linear regression of population. _a_. Regression of population on ln area. _b_. Regression of population on ln fishing miles.] The confidence intervals for the fishing-mile estimates may be obtained in similar fashion--simply substituting the words fishing mile for area and S_{f} for S_{a}. For calculating the confidence intervals for area we have the following quantities: [=X] = 5.56 t_{.2} = 1.533 =S=(X_i - [=X])^2 = .859 S_{a} = .3594 The calculations are shown in table 5. The comparable quantities in calculating the confidence intervals for fishing-mile estimates are: [=X] = 3.70 t_{.2} = 1.533 =S=(X_{i} - [=X])^2 = .932 S_{f} = .394 The calculations are shown in table 6. TABLE 5 _Calculation of Confidence Intervals for Area_ Column headings: A = X_{o} B = (X_{o} - [=X]) (X_{o} - [=X])^2 C = --------------------- =S=((X_{i} - [=X])^2) ___________________________ {1 (X_{o} - [=X])^2 } D = [Sqrt]{- + ---------------------} {6 =S=((X_{i} - [=X])^2)} ___________________________ {1 (X_{o} - [=X])^2 } E = t_{.2}S_{a} × Sqrt{- + ---------------------} {6 =S=((X_{i} - [=X])^2)} =========================================================== | Tribe | [A] [B] [C] [D] [E] ______________________|____________________________________ | Kato | 5.42 -.23 .0616 .4778 .263 Bear River | 4.80 -.83 .8510 1.0088 .556 Lassik | 5.96 .31 .1119 .5278 .291 Nongatl | 6.75 1.10 1.4086 1.2551 .692 Shelter Cove Sinkyone | 5.86 .21 .0513 .4669 .257 ______________________|____________________________________ TABLE 6 Calculation of Fishing-Mile Estimates Column headings: A = X_{o} B = (X_{o} - [=X]) C = --------------------- =S=((X_{i} - [=X])^2)