A study of pregnant grey seals involved n= 25 observations on the variables y = fetus pr...

A study of pregnant grey seals involved n= 25 observations on the variables y = fetus progesterone level (mg), x₁ = fetus 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 (“Gonadotrophin and Progesterone Concentration in Placenta of Grey Seals,” Journal of Reproduction and Fertility [1984]: 521– 528).

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 x₁ and x₂ in the model? Explain.

d. After elimination of both x₃ and x₁, the estimated regression equation is . The corresponding values of R² and se are .527 and 4.116, respectively. Interpret these values.

e. Referring to Part (d), how would you interpret the value of b₂ = .231? Does it make sense to interpret the value of a as the estimate of average progesterone level when length is zero? Explain.