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

1. a. Use information from the Minitab output to test the hypothesis H₀: β₁ = β₂ = β₃ = 0.
2. b. Using an elimination criterion of −2 ≤ t ratio ≤ 2, should any variable be eliminated? If so, which one?
3. 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%

1. d. After elimination of both x₃ and x₁, the estimated regression equation is ŷ = −2.61 + 0.231x₂. The corresponding values of R² and s_e are 0.527 and 4.116, respectively. Interpret these values.
2. 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.