Question

Botanists at the University of Toronto conducted a series of experiments to investigate the feeding habits of baby snow geese. Goslings were deprived of food until their guts were empty, then were allowed to feed for 6 hours on a diet of plants or Purina Duck Chow. For each of 42 feeding trials, the change in the weight of the gosling after 2.5 hours was recorded as a percentage of initial weight. Two other variables recorded were digestion efficiency (measured as a percentage) and amount of acid-detergent fiber in the digestive tract (also measured as a percentage). The data on gosling weight change, digestion efficiency, acid-detergent fiber (all measured as percentages) and diet (plants or duck chow) for 42 feeding trials are saved in the SNOWGEESE file. The botanists were interested in predicting weight change (y) as a function of digestion efficiency and aciddetergent fiber.

Trial   Diet   WtChange   DigEff   ADFiber
1   Plants   -6.0   0.0   28.5
2   Plants   -5.0   2.5   27.5
3   Plants   -4.5   5.0   27.5
4   Plants   0.0   0.0   32.5
5   Plants   2.0   0.0   32.0
6   Plants   3.5   1.0   30.0
7   Plants   -2.0   2.5   34.0
8   Plants   -2.5   10.0   36.5
9   Plants   -3.5   20.0   28.5
10   Plants   -2.5   12.5   29.0
11   Plants   -3.0   28.0   28.0
12   Plants   -8.5   30.0   28.0
13   Plants   -3.5   18.0   30.0
14   Plants   -3.0   15.0   31.0
15   Plants   -2.5   17.5   30.0
16   Plants   -0.5   18.0   22.0
17   Plants   0.0   23.0   22.5
18   Plants   1.0   20.0   24.0
19   Plants   2.0   15.0   23.0
20   Plants   6.0   31.0   21.0
21   Plants   2.0   15.0   24.0
22   Plants   2.0   21.0   23.0
23   Plants   2.5   30.0   22.5
24   Plants   2.5   33.0   23.0
25   Plants   0.0   27.5   30.5
26   Plants   0.5   29.0   31.0
27   Plants   -1.0   32.5   30.0
28   Plants   -3.0   42.0   24.0
29   Plants   -2.5   39.0   25.0
30   Plants   -2.0   35.5   25.0
31   Plants   0.5   39.0   20.0
32   Plants   5.5   39.0   18.5
33   Plants   7.5   50.0   15.0
34   Chow   0.0   62.5   8.0
35   Chow   0.0   63.0   8.0
36   Chow   2.0   69.0   7.0
37   Chow   8.0   42.5   7.5
38   Chow   9.0   59.0   8.5
39   Chow   12.0   52.5   8.0
40   Chow   8.5   75.0   6.0
41   Chow   10.5   72.5   6.5
42   Chow   14.0   69.0   7.0

a. Write a complete second order model for weight change (y).

Answer 1

The complete second order model for weight change (y) is:

WtChange = 1.530 - 2.86 DigEff_0.0 + 1.97 DigEff_1.0 - 5.03 DigEff_2.5 - 6.03 DigEff_5.0 - 4.03 DigEff_10.0 - 4.03 DigEff_12.5 - 1.20 DigEff_15.0 - 4.03 DigEff_17.5 - 3.53 DigEff_18.0 - 2.78 DigEff_20.0 + 0.47 DigEff_21.0 - 1.53 DigEff_23.0 - 1.53 DigEff_27.5 - 4.53 DigEff_28.0 - 1.03 DigEff_29.0 - 4.53 DigEff_30.0 + 4.47 DigEff_31.0 - 2.53 DigEff_32.5 + 0.97 DigEff_33.0 - 3.53 DigEff_35.5 - 0.36 DigEff_39.0 - 4.53 DigEff_42.0 + 6.47 DigEff_42.5 + 5.97 DigEff_50.0 + 10.47 DigEff_52.5 + 7.47 DigEff_59.0 - 1.53 DigEff_62.5 - 1.53 DigEff_63.0 + 6.47 DigEff_69.0 + 8.97 DigEff_72.5 + 6.97 DigEff_75.0