The article “Two Different Approaches for RDC Modelling When Simulating a Solvent Deasphalting Plant”

(J. Aparicio, M. Heronimo, et al., Computers and Chemical Engineering, 2002:1369–1377) reports flow rate (in dm3/h) and specific gravity measurements for a sample of paraffinic hydrocarbons. The natural logs of the flow rates

(y) and the specific gravity measurements (x) are presented in the following table.

y xy x

−1.204 0.8139 1.311 0.8264

−0.580 0.8171 1.959 0.8294 0.049 0.8202 2.614 0.8323 0.673 0.8233 3.270 0.8352

a. Fit the linear model y = ????0 + ????1x + ????. For each coefficient, test the hypothesis that the coefficient is equal to 0.

b. Fit the quadratic model y = ????0 + ????1x + ????2x2 + ????. For each coefficient, test the hypothesis that the coefficient is equal to 0

c. Fit the cubic model y = ????0 + ????1x + ????2x2 +????3x3 + ????. 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 flow rate when the specific gravity is 0.83.