Archaeology Inc.

The firm Archaeology Inc. is specialised in performing archaeological excavations in geographical areas that are designated to be developed for new construction works. In the last few years, the excavation business has become increasingly competitive. Most project developers select the archaeological company for doing the excavation in their site mostly based on lowest price offers. Mrs. Abinta, the controller of Archaeology Inc., has become increasingly aware of the importance of gaining sufficient economies of scale in her company.

During busy times, employees in Archaeology Inc. become flexible and perform many different tasks when required. Even back-office personnel sometimes join in to help in the excavation sites. Mrs. Abinta wonders whether it is possible to gain economies of scale in her company. She decides to analyse the average cost of archaeological excavation per hectare in the last year (50 weeks), which are the following:

Required:
1. Estimate a simple regression model for the average costs per hectare.
2. Comment on the quality of the relationship you found.
3. Adapt the regression function in order to capture the economies of scale effect.
4. Try to do the same as under ‘3’ using Excel’s line fitting possibilities. Which line fitting option should be choosen and why?

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Excavation costs Weeks Hectares Average Weeks cost per Hectares Average cost per hectare hectare 123456788 30 945 26 53 1730 46 1559 27 48 1425 62 1735 28 31 1109 69 1933 29 47 1884 44 1387 30 58 1710 57 1782 31 60 1809 48 1671 32 52 1743 66 1789 33 44 1595 36 1332 34 34 1084 10 53 1600 35 46 1441 11 62 1794 36 50 1497 12 47 1646 37 54 1563 13 70 1710 38 37 1186 14 32 872 39 65 1811 15 39 1206 40 42 1407 16 59 1716 41 51 1591 17 50 1700 42 57 1792 18 36 1030 43 53 1790 19 71 1811 44 49 1618 222222 20 50 1650 45 68 1833 21 46 1480 46 47 1648 57 1760 47 36 1153 23 66 1678 48 45 1293 24 42 1276 49 64 1869 25 47 1344 50 48 1675