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1. For Project 2, you will construct a proportionality model for one of the following scenarios. As a group (three or less), choose which of these scenarios (only one) that you would like to model.

SUPERSTARS HEART RATE – MAMMALS HEART RATE – BIRDS

LUMBER CUTTERS CREW RACING SHELLS DINOSAUR WEIGHT

2. Part A: Choose one of the above scenarios and do the following: (note: this is not for submission, but merely to get you started on the project):

a. Develop several possible Problem Identifications. Choose one and justify your choice. Hint: It should be one for which there is data provided to you to test your proportionality assumption.

b. List & briefly discuss the variables which influence the problem you have identified. Which do you think could be neglected in an initial analysis? Which appear to be critical?

3. Part B: After completing Part A, and within a few days, schedule a quick session with your instructor. During this session you should discuss your Part A solutions, and orally outline your approach to the problem. This approach includes the Model Development, i.e., the proportionality model itself. Normally, the session can be accomplished in less than 10 minutes.

4. Part C: SUBMISSION

a. Develop an explanatory model and prepare a report on your analysis. Your report should provide a discussion of each area of the Model Building Process (page 59 of text) and addresses the following specific topics:

1) Problem Identification statement

2) Make assumptions, identify and define variables

3) Develop the mathematical model based upon your assumptions.

4) State the final model form.

5) Test the model assumption of proportionality with the data. This is must be done with a graph. Discuss “how good” you think your model is.

6) State several strengths and weakness of the model that you designed.

7) Write a one page “executive summary” of your model results and put this as the first page after your title page.

8) Make a Title page.

b. Prepare a short presentation, about 10 minutes long. It should include the major assumptions, the final model, the proportionality graph, and any major strengths or weaknesses of the model.

As a minimum, your model development (step 3) should include :

a. Provide a brief appraisal of your model - how good do you think your assumptions are? How precise do you expect your results to be?

b. Include a graphical test of your model (submodels). A plot with discussion is REQUIRED.

c. Fit your model you developed with the data using the least squares criterion. Explain how you arrived at the coefficients. Discuss the meaning of the coefficient or coefficients.

d. Discuss how the different fitting criteria of the textbook could apply to your problem. If you could have chosen only one criteria, which one would you have chosen and why?

e. Answer all scenario-dependent questions!

Heart Rate - Birds

Warm-blooded animals use large quantities of energy to maintain body temperature because of the heat loss through the body surface. In fact, biologists believe that the primary energy drain on a resting warm-blooded animal is maintenance of body temperature.

a. Construct a model relating blood flow through the heart to body weight. Assume that the amount of energy available is proportional to the blood flow through the lungs, which is the source of oxygen. Assuming the least amount of blood needed to circulate, the amount of available energy will equal the amount of energy used to maintain the body temperature.

b. The following data relate weights of some type of birds to their heart rate measured in beats per minute. Construct a model that relates heart rate to body weight. Discuss the assumptions of your model. Use the data provided to check your model.

Bird Body Weight (g) Heart rate (Beats/min)

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Canary 20 1000

Pigeon 300 185

Crow 341 378

Buzzard 658 300

Duck 1100 190

Hen 2000 312

Goose 2300 240

Turkey 8750 193

Ostrich 71000 60-70

(data from A.J. Clark, Comparative Physiology of the Heart,(New York, Macmillian, 1977), p 99.)