Refer to the Journal of Applied Ecology (Vol. 32,1995) study of the feeding habits of baby snow geese, Exercise 9.56 (p. 514). 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 reproduced in the table above. The botanists were interested in predicting weight change (y) as a function of the other variables. The first-order model

 is digestion efficiency and x₂ is acid-detergent fiber, was fit to the data. The MINITAB printout is provided on page 578.

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

b. Interpret the ß-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 ß₂. Interpret the result.

e. Explain how to include the qualitative variable diet into the model

Exercise 9.56

Researchers at the University of Toronto conducted a series of experiments to investigate whether a commercially sold pet food could serve as a substitute diet for baby snow geese (Journal of Applied Ecology,Vol.32. 1995). Goslings were deprived of food until their guts I were empty, then were allowed to feed for 6 hours on i a diet of plants or Purina Duck Chow. For each feeding trial, the change in the weight of the gosling after 2.5 hours was recorded as a percentage of initial weight. ! Two other variables recorded were digestion efficiency (measured as a percentage) and amount of acid-detergent fiber in the digestive tract (also measured as a percentage). The data for 42 feeding trials are listed in the I table on page 517

a. The researchers were interested in the correlation between weight change (y) and digestion efficiency (x). I Plot the data for these two variables in a scattergram. Do you observe a trend?

b. On the SPSS printout on page 516, locate the coefficient of correlation relating weight change y to digestion efficiency x. Interpret this value.

c. Conduct a test (at α = .01) to determine whether weight change y is correlated with digestion efficiency x. (Note: The SPSS printout reports p-values for a test of the null hypothesis of zero correlation.)

d. Repeat parts b and c, but exclude the data for trials that used duck chow from the analysis. What do you t conclude?

e. The researchers were also interested in the correlation between digestion efficiency ('y) and acid-detergent fiber (x). Repeat parts a-d for these two variables.