Question

The length of a species of fish is to be represented as a function of the age (measured in days) and water temperature (degrees Celsius). The fish are kept in tanks at 25, 27, 29 and 31 degrees Celsius. After birth, a test specimen is chosen at random every 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 be appropriate given the shape of the residual plot? Logarithmic transformation in both Y and the X variables Quadratic transformation to correct for curvilinear relationship No transformation is necessary

Answer 1

Seeing the age residual plot, we can say there is a curvilinear relationship and to curb this we can do the quadratic transformation.