The article “Electrical Impedance Variation with Water Saturation in Rock” (Q. Su, Q. Feng, and Z. Shang, Geophysics, 2000:68–75) reports measurements of permeabilities (in 10−3????m2), porosities (in %), and surface area per unit volume of pore space (in 104 cm−1) for several rock samples. The results are presented in the following table, denoting ln Permeability by y, porosity by x1, and surface area per unit volume by x2.

y x1 x2 y x1 x2

−0.27 19.83 9.55 0.58 10.52 20.03 2.58 17.93 10.97 −0.56 18.92 13.10 3.18 21.27 31.02 −0.49 18.55 12.78 1.70 18.67 28.12 −0.01 13.72 40.28

−1.17 7.98 52.35 −1.71 9.12 53.67

−0.27 10.16 32.82 −0.12 14.39 26.75

−0.53 17.86 57.66 −0.92 11.38 75.62

−0.29 13.48 21.10 2.18 16.59 9.95 4.94 17.49 9.15 4.46 16.77 7.88 1.94 14.18 11.72 2.11 18.55 88.10 3.74 23.88 5.43 −0.04 18.02 10.95

a. Fit the model y = ????0 + ????1x1 + ????2x2 + ????3x1x2 + ????. Compute the analysis of variance table.

b. Fit the model y = ????0 + ????1x1 + ????2x2 + ????. Compute the analysis of variance table.

c. Fit the model y = ????0 + ????1x1 + ????. Compute the analysis of variance table.

d. Compute the F statistics for comparing the models in parts

(b) and

(c) with the model in part (a). Which model do you prefer? Why?