1. The data below came from the side of an Iams 40 pound bag of dog food. It gives the "best amount to feed your dog each day," based on the weight of your dog. This question reviews linear and allometric models, using Excel.
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Wt. of Dog, W
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Amt of Food, A
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10 lbs
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3/4 c.
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20 lbs
|
1 1/4
c.
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40 lbs
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1 3/4
c.
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60 lbs
|
2 1/3
c
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80 lbs
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2 3/4
c.
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100 lbs
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3 1/3
c.
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a. Try the simplest model by using Excel's Trendline to fit a linear model through the data. Graph the data and model for amount of food (A) as a function of the weight of the dog (W), so W is the independent variable. Give the formula for this best straight line model. How well does the graph fit the data? What happens to the model as the weight gets close to zero? Use this model to find how much you would feed a 5 lb dog and a 45 lb dog. What size of dog would consume 1 c. of food?
b. For this part of the problem use the power law under Excel's trendline to best fit the data. Plot the data and the best power law fit, then have Excel write the formula on your graph. What happens to this model as the weight gets close to zero? Use this model to find how much you would feed a 5 lb dog and a 45 lb dog. What size of dog would consume 1 c. of food?
c. Which of the two models is better and give a reason why? Can you provide any explanation for the power obtained in the second model?