Given the foregoing assumptions, the least squares estimate of the normal regression line may be obtained with the following formula.
P: population. A: area. F: fishing miles.
The equations of the lines are:
P = a + b (ln A)
P = a' + b' (ln F)
the estimate of b is (Bennett and Franklin, 1954, p. 224)
Σ(Xi − X̅)(Yi − Y̅)
b̂ = ------------------------------------
Σ(Xi − X)2
and of a is
â = Y̅ − b̂X̅
where Xi = ln A for each group with known population and Yi = P for each known group.
Similarly the estimate of b' is