Data set located just above. 5. If the Pilgrims had gone hunting for a turkey as
ID: 3259480 • Letter: D
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Data set located just above.
5. If the Pilgrims had gone hunting for a turkey as big as a large dog, turkey might not have become the meat of choice for traditional Thanksgiving meals today. The world's heaviest turkey on record weighed 86 pounds - about the size of a large German Shepherd and was grown more than three centuries later in England. according to Dr. Sarah Birkhold, poultry specialist with the Texas Agricultural Extension Service. The turkey hens consumed now are traditionally raised to 18 to 25 weeks of age and a weight 9 to 12 pounds of ready-to-cook meat. The toms (males) are raised to 22 to 30 weeks of age, and a weight of 20 pounds and up. So what exactly is the relationship between the weight and age of Thanksgiving turkeys? The data consists of turkey weigths (in pounds), and ages (in weeks) of 13 Thanksgiving turkeys. Four of these turkeys were reared in Georgia (G), four in Virginia (V), and five in Wisconsin (W). We would like to relate the weight to age via a simple straight line model, but the different origins of turkeys may cause a problem. One solution to this problem is to incorporate the origin of the turkeys in the model. The data are available in turkey.txt. (a) How would you include the state of origin in the model? Explicitly describe all the variables that go into your model. (b) Using clear statistical notation, write down the population equation of the model that regresses weight on age and state, including interaction. (c) Fit the model described in ?? and write the estimated regression equation here. (d) Based on this model, how much weight do turkeys reared in Georgia gain in one month, on average? (e) Do Gcorgia turkeys seem to gain weight more rapidly than turkeys from Wisconsin? Clearly write down (f) Using this model, compute a 95% prediction interval for the weight of a turkey reared in Virginia that is (g) Based on this analysis, is it plausible that the world's heaviest turkey on record was grown through the statistical hypothesis, provide a test statistic, p-value and a clearly stated conclusion. 26 weeks old natural methods?Explanation / Answer
a) How would you include the state of origin in the model? Explicitly describe all the variables that go into your model.
For Regression, we should have numeric variables and since ‘State of Origin’ is categorical with 3 categories, we will have to create Dummy Variables on it to bring it into model. Dummy variables will be like new variable specific to one of the category i.e. if the category is equal to Dummy var name, value would be ‘1’, else ‘0’. We need to create (No. of levels – 1) new dummy variables. In our case, Origin has 3 categories: G, V, and W. We will create two new dummy variables: Origin.G and Origin.V. If both of them have value 0, it would automatically mean origin is W.
So, the variable that will go in my model are: weight, origin.G, origin.V, age
(b) Using clear statistical notation, write down the population equation of the model that regresses weight on age and state, including interaction.
Without interaction term:
Weight = b0 + b1 * age + b2 * origin.G + b3 * origin.V + e
With interaction term:
Weight = b0 + b1 * age + b2 * origin.G + b3 * origin.V + b4 * age * origin.G + b4 * age * origin.V + e
Note: I am excluding interaction terms origin.G * origin.V and age * origin.G * origin.V as at a given time, either one or both of origin.V and origin.G will be 0 leading to interaction term to 0.
(c) Fit the model described in b and write the estimated regression equation here.
Estimated regression model without interaction term:
Estimated regression model with interaction term:
(d) Based on this model, how much weight do turkeys reared in Georgia gain in one month, on average?
Since interaction term between age and origin.G has coefficient of 0.13, so it means turkey in Georgia gain weight by 0.13 times in a year i.e. ( 0.13/12) in a month
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