Introduction To Statistics And Data Analysis
6th Edition
ISBN: 9781337793612
Author: PECK, Roxy.
Publisher: Cengage Learning,
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Chapter 14, Problem 70CR
A study of pregnant grey seals resulted in n = 25 observations on the variables y = Fetus progesterone level (mg), x1 = Felus sex (0 = male, 1 = female), x2 = Fetus length (cm), and x3 = Fetus weight (g). Minitab output for the model using all three independent variables is given (“Gonadotropin and Progesterone Concentration in Placenta of Grey Seals,” Journal of Reproduction and Fertility [1984]: 521–528).
The regression equation is Y = −1.98 − 1.87X1 + .234X2 + .0001X3
s = 4.189 R-sq = 55.2% R-sq(adj) = 48.8%
Analysis of Variance
- a. Use information from the Minitab output to test the hypothesis H0: β1 = β2 = β3 = 0.
- b. Using an elimination criterion of −2 ≤ t ratio ≤ 2, should any variable be eliminated? If so, which one?
- c. Minitab output for the regression using only x1 = Sex and x2 = Length is given. Would you recommend keeping both and x2 in the model? Explain.
The regression equation is Y = −2.09 − 1.87X1 + .240X2
s = 4.093 R-sq = 55.2% R-sq(adj) = 51.2%
- d. After elimination of both x3 and x1, the estimated regression equation is ŷ = −2.61 + 0.231x2. The corresponding values of R2 and se are 0.527 and 4.116, respectively. Interpret these values.
- e. Referring to Part (d), how would you interpret the value of b2 = 0.231? Does it make sense to interpret the value of a as the estimate of average progesterone level when length is zero? Explain.
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Chapter 14 Solutions
Introduction To Statistics And Data Analysis
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