The article “Modeling Resilient Modulus and Temperature Correction for Saudi Roads” (H. Wahhab, I. Asi, and R. Ramadhan, Journal of Materials in Civil Engineering, 2001:298–305) describes a study designed to predict the resilient modulus of pavement from physical properties. The following table presents data for the resilient modulus at 40◦C in 106 kPa (y), the surface area of the aggregate in m2/kg (x1), and the softening point of the asphalt in ◦C (x2).

y x1 x2 y x1 x2 y x1 x2 1.48 5.77 60.5 3.06 6.89 65.3 1.88 5.93 63.2 1.70 7.45 74.2 2.44 8.64 66.2 1.90 8.17 62.1 2.03 8.14 67.6 1.29 6.58 64.1 1.76 9.84 68.9 2.86 8.73 70.0 3.53 9.10 68.6 2.82 7.17 72.2 2.43 7.12 64.6 1.04 8.06 58.8 1.00 7.78 54.1 The full quadratic model is y = ????0 + ????1x1 + ????2x2 + ????3x1x2 + ????4x2 1 + ????5x2 2 + ????. Which submodel of this full model do you believe is most appropriate? Justify your answer by fitting two or more models and comparing the results.