Thus, given either the area of a group or the fishing miles of a group
habitat, we may estimate its population. From the diagram in figure 2 it
appears that the estimates based on area have greater dispersion than
those based on fishing miles and are therefore less reliable. This fact
can best be made precise by using the above assumptions to obtain the
confidence intervals for each of the estimates. The confidence intervals
for the area estimates are given by the following formula (Bennett and
Franklin, 1954, p. 229).
_______________________
{1 (X_o - [=X])^2 }
1.02 X_o - 4.06 ± t_[oc]S_a × [Sqrt]{- + -----------------}
{6 =S=(X_i - [=X])^2}
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