The article Influence of Freezing Temperature on Hydraulic Conductivity of Silty Clay (J. Konrad and M. Samson,

The article €œInfluence of Freezing Temperature on Hydraulic Conductivity of Silty Clay€ (J. Konrad and M. Samson, Journal of Geotechnical and Geoenvironmental Engineering, 2000:180€“187) describes a study of factors affecting hydraulic conductivity of soils. The measurements of hydraulic conductivity in units of 10ˆ’8 cm/s (y), initial void ratio (x1), and thawed void ratio (x₂) for 12 specimens of silty clay are presented in the following table.

a. Fit the model y = β₀ + β₁x₁ + ε. For each coefficient, test the null hypothesis that it is equal to 0.

b. Fit the model y = β₀ + β₁x₂ + ε. For each coefficient, test the null hypothesis that it is equal to 0.

c. Fit the model y = β₀ + β₁x₁ + β₂x₂ + ε. For each coefficient, test the null hypothesis that it is equal to 0.

d. Which of the models in parts (a) to (c) is the best of the three? Why do you think so?

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1.01 У X1 0.955 1.23 1.28 1.23 1.15 0.89 0.86 1.12 0.88 0.85 1.04 1.30 0.95 0.92 1.01 1.04 0.86 0.85 1.30 0.90 0.92 0.84 0.85 0.88 0.85 0.85 0.90 0.94 0.92 0.88 0.87 0.85 0.81 0.84 0.88 х,