The article ??Effect of Granular Subbase Thickness on Airfield Pavement Structural Response?? (K. Gopalakrishnan and M. Thompson, Journal of Materials in Civil Engineering, 2008:331??342) presents a study of the amount of surface deflection caused by aircraft landing on an airport runway. A load of 160 kN was applied to a runway surface, and the amount of deflection in mm (y) was measured at various distances in m (x) from the point of application. The results are presented in the following table.

a. Fit the linear model y = β₀ + β₁x + ε. For each coefficient, test the hypothesis that the coefficient is equal to 0.

b. Fit the quadratic model y = β₀ + β₁x + β₂x² + ε. For each coefficient, test the hypothesis that the coefficient is equal to 0.

c. Fit the cubic model y = β₀ +β₁x +β₂x² +β₃x³ +ε. For each coefficient, test the hypothesis that the coefficient is equal to 0.

d. Which of the models in parts (a) through (c) is the most appropriate? Explain.

e. Using the most appropriate model, estimate the deflection at a distance of 1 m.

y 0.000 0.305 0.610 0.914 3.24 2.36 1.42 0.87 1.219 0.54 1.524 0.34 1.830 0.24