Snow gees feeding trial. Botanists at the University of Toronto conducted a seri
ID: 3124344 • Letter: S
Question
Snow gees feeding trial. Botanists at the University of Toronto conducted a series of experiments to investigate the feeding habits of baby snow geese (Journal of Applied Ecology, Vol. 32, 1995). 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, the change in the weight of 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-detergen fiber in the digestive tract (also measured as a percentage). The data for selected feeding trials are listed below. The full data set is called SNOWGEESE in the data CD.
SNOWGEESE (First and last three trials)
Feeding Trial
Diet
Weight Change (%)
Digestion Efficiency (%)
Acid-detergent fiber (%)
1
Plants
-6
0
28.5
2
Plants
-5
2.5
27.5
3
Plants
- 4.5
5
27.5
40
Duck Chow
8.5
75
6
41
Duck Chow
10.5
72.5
6.5
42
Duck Chow
14
69
7
The botanists were interested in predicting weight change (y) as a function of the other variables. The first-order model E(y) = 0 + 1x1 + 2x2 , where x1 is digestion efficiency and x2 is acid-detergent fiber, was fit to the data. The MINITAB printout is given below.
-----------------------------------------------------------
Regression Analysis: WtChange versus DigEff, ADFiber
The regression equation is
WtChange = 12.2 - 0.0265 DigEff - 0.458 ADFiber
Term Coef SE Coef T P 99% CI Constant 12.1804 4.40236 2.76680 0.009 ( 0.259232, 24.1016) DigEff -0.0265 0.05349 -0.49618 0.623 (-0.171379, 0.1183)
ADFiber -0.4578 0.12828 -3.56914 0.001 (-0.805194, -0.1105) S = 3.51948 R-Sq = 52.9% R-Sq(adj) = 50.5%
Analysis of Variance
Source DF SS MS F P
Regression 2 542.03 271.02 21.88 0.000
Residual Error 39 483.08 12.39
Total 41 1025.12 -----------------------------------------------------------
(a)
Find the confidence interval for E(y) when x1=40% and x2=15%. Interpret the
confidence interval.
Feeding Trial
Diet
Weight Change (%)
Digestion Efficiency (%)
Acid-detergent fiber (%)
1
Plants
-6
0
28.5
2
Plants
-5
2.5
27.5
3
Plants
- 4.5
5
27.5
40
Duck Chow
8.5
75
6
41
Duck Chow
10.5
72.5
6.5
42
Duck Chow
14
69
7
Explanation / Answer
(a)
Find the confidence interval for E(y) when x1=40% and x2=15%. Interpret the confidence interval.
99% CI for x1=40% and x2=15%. = (2.15, 6.35).
We are 99% confident that weight change will fall in the interval (2.15, 6.35) when digestion efficiency(x1) is 40% and acid-detergent fiber(x2) is 15%.
Regression Analysis
R²
0.529
Adjusted R²
0.505
n
42
R
0.727
k
2
Std. Error
3.519
Dep. Var.
wtchange
ANOVA table
Source
SS
df
MS
F
p-value
Regression
542.0349
2
271.0174
21.88
4.25E-07
Residual
483.0842
39
12.3868
Total
1,025.1190
41
Regression output
confidence interval
variables
coefficients
std. error
t (df=39)
p-value
99% lower
99% upper
Intercept
12.1804
4.4024
2.767
.0086
0.2592
24.1016
digeff
-0.0265
0.0535
-0.496
.6226
-0.1714
0.1183
adfibr
-0.4578
0.1283
-3.569
.0010
-0.8052
-0.1105
Predicted values for: wtchange
99% Confidence Interval
99% Prediction Interval
digeff
adfibr
Predicted
lower
upper
lower
upper
Leverage
40
15
4.2514
2.1511
6.3516
-5.5078
14.0105
0.049
Regression Analysis
R²
0.529
Adjusted R²
0.505
n
42
R
0.727
k
2
Std. Error
3.519
Dep. Var.
wtchange
ANOVA table
Source
SS
df
MS
F
p-value
Regression
542.0349
2
271.0174
21.88
4.25E-07
Residual
483.0842
39
12.3868
Total
1,025.1190
41
Regression output
confidence interval
variables
coefficients
std. error
t (df=39)
p-value
99% lower
99% upper
Intercept
12.1804
4.4024
2.767
.0086
0.2592
24.1016
digeff
-0.0265
0.0535
-0.496
.6226
-0.1714
0.1183
adfibr
-0.4578
0.1283
-3.569
.0010
-0.8052
-0.1105
Predicted values for: wtchange
99% Confidence Interval
99% Prediction Interval
digeff
adfibr
Predicted
lower
upper
lower
upper
Leverage
40
15
4.2514
2.1511
6.3516
-5.5078
14.0105
0.049
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