Chapter 8, Problem 15SE

The article “Measurements of the Thermal Conductivity and Thermal Diffusivity of Polymer Melts with the Short-Hot-Wire Method” (X. Zhang, W. Hendro, et al., International Journal of Thermophysics, 2002:1077–1090) reports measurements of the thermal conductivity (in W · m^–1 · K^–1) and diffusivity of several polymers at several temperatures (in 1000 C). The following table presents results for the thermal conductivity of polycarbonate.

1. a. Denoting conductivity by y and temperature by x. fit the linear model $y={\beta }_0+{\beta }_{1}x+\epsilon$. For each coefficient, test the hypothesis that the coefficient is equal to 0.
2. b. Fit the quadratic model $y={\beta }_0+{\beta }_{1}x+{\beta }_2{x}^2+\epsilon$. For each coefficient, test the hypothesis that the coefficient is equal to 0.
3. c. Fit the cubic model $y={\beta }_0+{\beta }_{1}x+{\beta }_2{x}^2+{\beta }_3{x}^3+\epsilon$. For each coefficient, test the hypothesis that the coefficient is equal to 0.
4. d. Fit the quartic model $y={\beta }_0+{\beta }_{1}x+{\beta }_2{x}^2+{\beta }_3{x}^3+{\beta }_4{x}^4+\epsilon$. For each coefficient, test the hypothesis that the coefficient is equal to 0.
5. e. Which of the models in parts (a) through (d) is the most appropriate? Explain.
6. f. Using the most appropriate model, estimate the conductivity at a temperature of 120°C.