The length of a species of fish is to be represented as afunction of the age (measured in days) and water temperature(degrees Celsius). The fish are kept in tanks at 25, 27, 29 and 31degrees Celsius. After birth, a test specimen is chosen at randomevery 14 days and its length measured.
| Age | Temp | Length |
1 | 14 | 25 | 620 |
2 | 28 | 25 | 1,315 |
3 | 41 | 25 | 2,120 |
4 | 55 | 25 | 2,600 |
5 | 69 | 25 | 3,110 |
6 | 83 | 25 | 3,535 |
7 | 97 | 25 | 3,935 |
8 | 111 | 25 | 4,465 |
9 | 125 | 25 | 4,530 |
10 | 139 | 25 | 4,570 |
11 | 153 | 25 | 4,600 |
12 | 14 | 27 | 625 |
13 | 28 | 27 | 1,215 |
14 | 41 | 27 | 2,110 |
15 | 55 | 27 | 2,805 |
16 | 69 | 27 | 3,255 |
17 | 83 | 27 | 4,015 |
18 | 97 | 27 | 4,315 |
19 | 111 | 27 | 4,495 |
20 | 125 | 27 | 4,535 |
21 | 139 | 27 | 4,600 |
22 | 153 | 27 | 4,600 |
23 | 14 | 29 | 590 |
24 | 28 | 29 | 1,305 |
25 | 41 | 29 | 2,140 |
26 | 55 | 29 | 2,890 |
27 | 69 | 29 | 3,920 |
28 | 83 | 29 | 3,920 |
29 | 97 | 29 | 4,515 |
30 | 111 | 29 | 4,520 |
31 | 125 | 29 | 4,525 |
32 | 139 | 29 | 4,565 |
33 | 153 | 29 | 4,566 |
34 | 14 | 31 | 590 |
35 | 28 | 31 | 1,205 |
36 | 41 | 31 | 1,915 |
37 | 55 | 31 | 2,140 |
38 | 69 | 31 | 2,710 |
39 | 83 | 31 | 3,020 |
40 | 97 | 31 | 3,030 |
41 | 111 | 31 | 3,040 |
42 | 125 | 31 | 3,180 |
43 | 139 | 31 | 3,257 |
44 | 153 | 31 | 3,214 |
Which of the following types of transformation may beappropriate given the shape of the residual plot? | | Logarithmic transformation in both Y and the X variables | | | Quadratic transformation to correct for curvilinearrelationship | | | No transformation is necessary |
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