{1 (Xo − X̅)2 }
1.02 Xo − 4.06 ± t∝Sa × √{- + -----------}
{6 Σ(Xi − X̅)2}
where the symbols have the following values and meanings:
[10.6] Xo: the log of the area of the group for which the population is being estimated.
Xi: the log of the area of each of the groups for which the population is already known.
X̅: the average of the Xi.
t∝: the upper ∝-point of the t-distribution (Bennett and Franklin, 1954, p. 696) where 1-∝ is the confidence coefficient.
{1 }
Sa = √{- × Σ(Yi + 4.06 − 1.02Xi)2}
{4 }where Yi 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.
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 Sf for Sa.
For calculating the confidence intervals for area we have the following quantities:
X̅ = 5.56
t.2 = 1.533
Σ(Xi − X̅)2 = .859
Sa = .3594
The calculations are shown in table 5.
The comparable quantities in calculating the confidence intervals for fishing-mile estimates are: