Moissanite is a popular abrasive material because of its extreme hardness. Another important property of moissanite is elasticity. The elastic properties of the material were investigated in the Journal of Applied Physics (Sept. 1993). A diamond anvil cell was used to compress a mixture of moissanite, sodium chloride, and gold in a ratio of 33:99:1 by volume. The compressed volume, y, of the mixture (relative to the zero pressure volume) was measured at each of 11 different pressures (GPa). The results are displayed in the table below.

a. Fit the straight-line regression model E(y) = β_o + β₁x to the data.

b. Calculate the regression residuals for this model.

c. Plot the residuals against x. Do you detect a trend?

d. Propose an alternative model based on the plot, part c.

e. Fit and analyze the model, part d.

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ELASTICITY Compressed Volume y, % Pressure x, GPa volume y, % Pressure x, GPa Compressed 100 85.2 51.6 96 9.4 83.3 60.1 93.8 15.8 82.9 62.6 90.2 30.4 82.9 62.6 87.7 41.6 81.7 68.4 86.2 46.9