The article ??Low-Temperature Heat Capacity and Thermodynamic Properties of 1,1,1-trifluoro-2, 2-dichloroethane?? (R. Varushchenko and A. Druzhinina, Fluid Phase Equilibria, 2002:109??119) presents measurements of the molar heat capacity (y) of 1,1,1-trifluoro-2,2-dichloroethane (in J ? K??1 ? mol??1) at several temperatures (x) in units of 10 K. The results for every tenth measurement are presented in the following table.

a. Fit the simple linear model y = β₀ + β₁x + ε. Make a residual plot, and comment on the appropriateness of the model.

b. Fit the simple linear model y = β₀ + β₁ ln x + ε. Make a residual plot, and comment on the appropriateness of the model.

c. Compute the coefficients and their standard deviations for polynomials of degrees 2, 3, 4, and 5. Make residual plots for each.

d. The article cited at the beginning of this exercise recommends the quartic model y = β₀ +β₁x +β₂x² + β₃x³ + β₄x⁴ + ε. Does this seem reasonable? Why or why not?

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y y 5.7037 1.044 60.732 6.765 16.707 1.687 65.042 7.798 9.241 10.214 29.717 2.531 71.283 41.005 48.822 55.334 3.604 75.822 80.029 4.669 11.266 5.722