In the book Analysis of Longitudinal Data, 2nd ed., (2002, Oxford University Press), by Diggle, Heagerty, Liang,and Zeger, the authors analyzed the effects of three diets on the protein content of cow's milk. The data shown here were collected after one week and include 25 cows on the barley diet and 27 cows each on the other two diets: Diet Barley Protein content of cow's milk 3.63 3.24 3.98 3.66 4.34 4.36 4.17 4.4 3.4 3.75 4.2 4.02 4.02 3.9 3.81 3.62 3.66 Barley+Lupins 3.38 3.8 3.8 4.59 4.07 4.32 3.56 3.67 4.15 3.51 4.2 4.12 3.52 4.08 4.02 3.18 4.11 3.69 4.2 4.2 3.13 3.73 4.32 3.04 3.84 3.98 4.18 4.2 4.1 3.25 3.34 3.5 4.13 3.21 Lupins

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In the book Analysis of Longitudinal Data, 2nd ed., (2002, Oxford University Press), by Diggle, Heagerty, Liang,and Zeger, the authors
analyzed the effects of three diets on the protein content of cow's milk. The data shown here were collected after one week and
include 25 cows on the barley diet and 27 cows each on the other two diets:
Diet
Barley
Protein content of cow's milk
Lupins
3.63 3.24 3.98 3.66 4.34 4.36 4.17 4.4 3.4 3.75 4.2 4.02 4.02 3.9 3.81 3.62 3.66
Barley+Lupins 3.38 3.8 3.8 4.59 4.07 4.32 3.56 3.67 4.15 3.51 4.2 4.12 3.52 4.08 4.02 3.18 4.11
3.69 4.2 4.2 3.13 3.73 4.32 3.04 3.84 3.98 4.18 4.2 4.1 3.25 3.34 3.5
4.13 3.21
Transcribed Image Text:In the book Analysis of Longitudinal Data, 2nd ed., (2002, Oxford University Press), by Diggle, Heagerty, Liang,and Zeger, the authors analyzed the effects of three diets on the protein content of cow's milk. The data shown here were collected after one week and include 25 cows on the barley diet and 27 cows each on the other two diets: Diet Barley Protein content of cow's milk Lupins 3.63 3.24 3.98 3.66 4.34 4.36 4.17 4.4 3.4 3.75 4.2 4.02 4.02 3.9 3.81 3.62 3.66 Barley+Lupins 3.38 3.8 3.8 4.59 4.07 4.32 3.56 3.67 4.15 3.51 4.2 4.12 3.52 4.08 4.02 3.18 4.11 3.69 4.2 4.2 3.13 3.73 4.32 3.04 3.84 3.98 4.18 4.2 4.1 3.25 3.34 3.5 4.13 3.21
(a) What is the P-value from the ANOVA table?
Round your answer to three decimal places (e.g. 98.765).
P-value= i
(b) Does diet affect the protein content of cow's milk? Use a = 0.05 and the P-value to make this inference.
(c) Estimate variability due to random errors.
Round your answer to three decimal places (e.g. 98.765).
az
²
O Yes, diet affects the protein content.
O No, diet does not affect the protein content.
= i
(d) In the following plots, some are used to analyze the residuals. From these plots, select the plot of residuals versus fitted
values.
O
1,0
0,5
0,0
-0,5
-1,0-
3
2
1
0
-1
-2
-3
4.5
4.0
3.5-
3.0-
2.5
1.0
0.5
0.0
-0.5
-1.0
1
MOMO
●●●●
.
3,80
-1.0
C1
5 10
3,82
-0.5
0.0
3,84
C2
Normal
***** ****
0.5
3,86
20 30 40 50 60 70 80
1.0
C3
3,88
90 95
me m
**
1.5
99
Transcribed Image Text:(a) What is the P-value from the ANOVA table? Round your answer to three decimal places (e.g. 98.765). P-value= i (b) Does diet affect the protein content of cow's milk? Use a = 0.05 and the P-value to make this inference. (c) Estimate variability due to random errors. Round your answer to three decimal places (e.g. 98.765). az ² O Yes, diet affects the protein content. O No, diet does not affect the protein content. = i (d) In the following plots, some are used to analyze the residuals. From these plots, select the plot of residuals versus fitted values. O 1,0 0,5 0,0 -0,5 -1,0- 3 2 1 0 -1 -2 -3 4.5 4.0 3.5- 3.0- 2.5 1.0 0.5 0.0 -0.5 -1.0 1 MOMO ●●●● . 3,80 -1.0 C1 5 10 3,82 -0.5 0.0 3,84 C2 Normal ***** **** 0.5 3,86 20 30 40 50 60 70 80 1.0 C3 3,88 90 95 me m ** 1.5 99
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