The first task for Group 4 was to take the extrapolations done by Group 3 and apply them to the binned occurrence rate data produced by Group 2. In order to estimate the occurrence rate of Earth-sized planets in the habitable zone, we used the trends found by Group 3 to extrapolate an occurrence rate for planets with incoming flux between 0.25-1 \({F_\oplus}\). We altered the edges of the flux and radius boxes so that the boundaries were 0.25-512 \({F_\oplus}\) and 1-16 \({R_\oplus}\).
We attempted the extrapolation in two different ways. For the first method, we used a weighted average of the bins that fit the linear trend provided by group 3, which was approximated by averaging the bins less than 8 \({F_\oplus}\). We assumed these same values for the 0.25-0.5 \({F_\oplus}\) and the 0.5-1 \({F_\oplus}\) boxes. After adding up the percentages in these two boxes for 1-2 \({R_\oplus}\), we got an occurrence rate of 3.84%, which is much lower than Petigura found.
For the second method, we assumed that the lower flux boxes had incorrect completeness. At higher fluxes, there were many more of the lower radii planets than at lower fluxes. It would be harder to detect low radius planets at low fluxes, so it follows that many of the small radius planets may have been missed. Therefore, we took the weighted average of the percentages at the higher fluxes (32-512 \({F_\oplus}\)) for each row from 1-4 \({R_\oplus}\). The final values, which had extremely large errors, were: 0.29 \(\pm\) 6.7% for 2.8-4 \({R_\oplus}\), 0.18 \(\pm\) 2.07% for 2-2.8 \({R_\oplus}\), 0.40 \(\pm\) 2.44% for 1.4-2 \({R_\oplus}\), and 0.69 \(\pm\) 1.53% for 1-1.4 \({R_\oplus}\). We found the proportions between these values, and then used the same proportionality for the lower flux boxes. We chose the 2-2.8 \({F_\oplus}\) box (of 3.84%) as the one to base the other values on, because it appeared to be the most complete. When we used this method of extrapolation, we found that the 2.8-4 \({R_\oplus}\) box was 5.25%, the 1.4-2 \({R_\oplus}\) box was 7.24%, and the 1-1.4 \({R_\oplus}\) box was 12.50%. Adding up the boxes from 1-2 \({R_\oplus}\) and 0.25-1 \({F_\oplus}\) gave a final value of 39.48%, which is much higher than Petigura’s value.