The Journal of Applied Ecology (Vol. 32, 1995) published a study of the feeding habits of baby snow geese. The data on gosling weight change, digestion efficiency, acid-detergent fiber (all measured as percentages) and diet (plants or duck chow) for 42 feeding trials are saved in the SNOWGEESE file. Selected observations are shown in the following table. The botanists were interested in predicting weight change (y) as a function of the other variables. Consider the first-order model E(y) = β_o + β₁x + β₂x², where x₁ is digestion efficiency and x₂ is acid-detergent fiber.

a. Find the least-squares prediction equation for weight change, y.

b. Interpret the β-estimates in the equation, part a.

c. Conduct a test to determine if digestion efficiency, x₁, is a useful linear predictor of weight change. Use α = .01.

d. Form a 99% confidence interval for β₂. Interpret the result.

e. Find and interpret R² and R_a². Which statistic is the preferred measure of model fit? Explain.

f. Is the overall model statistically useful for predicting weight change? Test using α = .05.    

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SNOWGEESE (First and last five trials shown) Weight Change (%) Digestion Efficiency (%) Acid- Feeding Trial Detergent Fiber (%) Diet 1 Plants -6 28.5 Plants -5 2.5 27.5 3 Plants -4.5 27.5 4 Plants 32.5 5 Plants 2 32 38 Duck Chow 9 59 8.5 39 Duck Chow 12 52.5 8 40 Duck Chow 8.5 75 6 41 Duck Chow 10.5 72.5 6.5 42 Duck Chow 14 69 7 ... 2.