The article Electrical ImpedanceVariation withWater Saturation in Rock (Q. Su, Q. Feng, and Z. Shang, Geophysics, 2000:6875)

The article €œElectrical ImpedanceVariation withWater Saturation in Rock€ (Q. Su, Q. Feng, and Z. Shang, Geophysics, 2000:68€“75) reports measurements of permeabilities (in 10ˆ’3μm2), porosities (in percent), and surface area per unit volume of pore space (in 104 cmˆ’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.

a. Fit the model y = β₀ + β₁x₁ + β₂x₂ + β₃x₁x₂ + ε. Compute the analysis of variance table.

b. Fit the model y = β₀ + β₁x₁ + β₂x₂ + ε. Compute the analysis of variance table.

c. Fit the model y = β₀ + β₁x₁ + ε. 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?

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y 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 18.67 7.98 1.70 28.12 -0.01 13.72 40.28 -1.17 52.35 -1.71 9.12 53.67 -0.27 -0.53 10.16 32.82 -0.12 14.39 26.75 17.86 57.66 -0.92 11.38 75.62 21.10 9.15 11.72 -0.29 13.48 2.18 16.59 9.95 4.94 17.49 4.46 16.77 7.88 1.94 14.18 2.11 18.55 88.10 3.74 23.88 5.43 -0.04 18.02 10.95