An article in the Journal of Pharmaceuticals Sciences (Vol. 80, 1991, pp. 971€“977) presents data on the observed mole fraction solubility of a solute at a constant temperature and the dispersion, dipolar, and hydrogen bonding Hansen partial solubility parameters. The data are as shown in the following table, where y is the negative logarithm of the mole fraction solubility, x1 is the dispersion partial solubility, x2 is the dipolar partial solubility, and x3 is the hydrogen bonding partial solubility.
(a) Fit the model Y = BP + B1X1 + B2X2 + B3X3 + B12X1X2 + B13X1X3 +B23X2X3 + B11X2/1 +B22X2/2 + B33X2/2 +E
(b) Test for significance of regression using a = 0.05.
(c) Plot the residuals and comment on model adequacy.
(d) Use the extra sum of squares method to test the contribution of the second-order terms using a = 0.05.

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Observation Number X2 0.22200 7.3 0.0 0.0 0.39500 8.7 0.0 0.3 3. 0.42200 8.8 0.7 1.0 4 0.43700 8.1 4.0 0.2 0.42800 9.0 0.5 1.0 0.46700 8.7 1.5 2.8 6. 9.3 0.44400 2.1 1.0 5.1 0.37800 7.6 3.4 0.49400 10.0 0.0 0.3 0.45600 10 8.4 3.7 4.1 3.6 2.0 11 0.45200 9.3 12 0.11200 7.7 2.8 7.1 13 0.43200 9.8 4.2 2.0 14 0.10100 7.3 2.5 6.8 15 8.5 2.0 0.23200 6.6 16 0.30600 9.5 2.5 5.0 17 0.09230 7.4 2.8 7.8 18 0.11600 7.8 2.8 7.7 0.07640 7.7 3.0 19 8.0 1.7 20 0.43900 10.3 4.2 21 0.09440 7.8 3.3 8.5 7.1 22 0.11700 3.9 6.6 23 0.07260 7.7 4.3 9.5 10.9 24 0.04120 7.4 6.0 25 0.25100 7.3 2.0 5.2 26 20.7 0.00002 7.6 7.8