Σ(Xi − X̅)(Yi − Y̅)
b̂' = ----------------------------------
Σ(Xi − X̅)2
and of a' is
â' = Y̅ − b̂'X̅
where Xi = ln F for each known group and Yi = P for each known group. These calculations are shown in table 4.
TABLE 4
Calculation of Regression Lines Shown in Figure 2
| Fishing Miles | ||||
| (Xi − X̅) | (Yi − Y̅) | (Xi − X̅)·(Yi − Y̅) | (Xi − X̅)2 | |
| -.452 | -.027 | .012 | .204 | |
| -.882 | -.579 | .511 | .778 | |
| .058 | -.483 | -.028 | .003 | |
| .548 | .393 | .215 | .300 | |
| .068 | -.208 | -.014 | .005 | |
| .658 | .905 | .595 | .433 | |
| Total. | ... | ... | 1.291 | 1.723 |
| Area | ||||
| (Xi − X̅) | (Yi − Y̅) | (Xi − X̅)·(Yi − Y̅) | (Xi − X̅)2 | |
| .041 | -.027 | -.001 | .002 | |
| -.445 | .579 | .258 | .198 | |
| -.514 | -.483 | .248 | .264 | |
| .034 | .393 | .013 | .001 | |
| .400 | -.208 | -.083 | .160 | |
| .484 | .905 | .438 | .234 | |
| Total. | ... | ... | .873 | .859 |
The results are the following equations, which are shown, together with the points from which they were calculated, on figure 2.
P = 1.02 (ln A) − 4.06
P = .75 (ln F) − 1.00
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).