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(See Solution) Snow geese feeding trial. The Journal of Applied Ecology (Vol. 32, 1995) published a study of the feeding habits of baby snow geese. The

Question: Snow geese feeding trial. 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) = \({{\beta }_{0}}+{{\beta }_{1}}{{x}_{1}}+{{\beta }_{2}}{{x}_{2}}\) , where x 1 is digestion efficiency and x 2 is acid-detergent fiber.

  1. Find the least-squares prediction equation for weight change, y.
    Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
    Intercept -6.45439 18.03466 -0.35789 0.730976 -49.0995 36.19077
    x1 0.243478 0.208613 1.167126 0.281374 -0.24981 0.736769
    x2 0.12694 0.601197 0.211146 0.838789 -1.29466 1.548543

    This means that the model is
    \[y=-6.45439+0.243478\,{{x}_{1}}+0.12694\,{{x}_{2}}\]
  2. Interpret the \(\beta \) -estimates in the equation, part a.
  3. Conduct a test to determine if digestion efficiency, x 1 , is a useful linear predictor of weight change. Use \(\alpha \) = .01.
  4. Form a 99% confidence interval for \({{\beta }_{2}}\). Interpret the result.
    Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0%
    Intercept -6.45439 18.03466 -0.35789 0.730976 -49.0995 36.19077 -69.5663 56.65755
    x1 0.243478 0.208613 1.167126 0.281374 -0.24981 0.736769 -0.48656 0.973516
    x2 0.12694 0.601197 0.211146 0.838789 -1.29466 1.548543 -1.97694 2.230816

    which means that the 99% confidence interval is (-1.9769, 2.2309)
  5. Find and interpret R 2 and R a 2 . Which statistic is the preferred measure of model fit? Explain.
  6. Is the overall model statistically useful for predicting weight change? Test using \(\alpha \) = .05.

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