3. The dataset butterfat in the package faraway contains the average butterfat content (percent- ages) of milk for random samples of twenty cows, ten two-year old and ten mature (greater than four years old), from each of five breeds. Therefore, for each combination of breed and age categories, there are ten observations. The data are from Canadian records of pure-bred dairy cattle. Questions of interest are (i) if butterfat content differs with age and/or breed, and (ii) if any potential breed effect is the same for the two age groups. (a) Make appropriate plots of the data and comment on them. (b) Determine an appropriate model, and write it down mathematically, to answer the questions of interest. What are your conclusions? (c) Is the best breed in terms of butterfat content clearly superior to the second best breed? Justify.

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3. The dataset butterfat in the package faraway contains the average butterfat content (percent-
ages) of milk for random samples of twenty cows, ten two-year old and ten mature (greater than four
years old), from each of five breeds. Therefore, for each combination of breed and age categories,
there are ten observations. The data are from Canadian records of pure-bred dairy cattle. Questions of
interest are (i) if butterfat content differs with age and/or breed, and (ii) if any potential breed effect is
the same for the two age groups.
(a) Make appropriate plots of the data and comment on them.
(b) Determine an appropriate model, and write it down mathematically, to answer the questions of
interest. What are your conclusions?
(c) Is the best breed in terms of butterfat content clearly superior to the second best breed? Justify.
Transcribed Image Text:3. The dataset butterfat in the package faraway contains the average butterfat content (percent- ages) of milk for random samples of twenty cows, ten two-year old and ten mature (greater than four years old), from each of five breeds. Therefore, for each combination of breed and age categories, there are ten observations. The data are from Canadian records of pure-bred dairy cattle. Questions of interest are (i) if butterfat content differs with age and/or breed, and (ii) if any potential breed effect is the same for the two age groups. (a) Make appropriate plots of the data and comment on them. (b) Determine an appropriate model, and write it down mathematically, to answer the questions of interest. What are your conclusions? (c) Is the best breed in terms of butterfat content clearly superior to the second best breed? Justify.
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