An article in the Journal of Pharmaceutical Sciences \((\mathbf{8 0}, 971-977,1991)\) presents data on the observed mole fraction solubility of a solute at a constant temperature, along with \(x_{1}=\) dispersion partial solubility, \(x_{2}=\) dipolar partial solubility, and \(x_{3}=\) hydrogen bonding Hansen partial solubility. The response \(y\) is the negative logarithm of the mole fraction solubility.
a. Fit a complete quadratic model to the data.
b. Test for significance of regression, and construct \(t\) statistics for each model parameter. Interpret these results.
c. Plot residuals and comment on model adequacy.

d. Use the extra-sum-of-squares method to test the contribution of all secondorder terms to the model.

Transcribed Image Text:

Observation Number y X1 2 X3 15 17 19 -23456789DULEHELERA 1 0.22200 7.3 0.0 0.0 0.39500 8.7 0.0 0.3 0.42200 8.8 0.7 1.0 0.43700 8.1 4.0 0.2 0.42800 9.0 0.5 1.0 0.46700 8.7 1.5 2.8 0.44400 9.3 2.1 1.0 0.37800 7.6 5.1 3.4 0.49400 10.0 0.0 0.3 10 0.45600 8.4 3.7 4.1 11 0.45200 9.3 3.6 2.0 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 0.23200 8.5 2.0 6.6 16 0.30600 9.5 2.5 5.0 0.09230 7.4 2.8 7.8 18 0.11600 7.8 2.8 7.7 0.07640 7.7 3.0 8.0 20 0.43900 10.3 1.7 4.2 21 0.09440 7.8 3.3 8.5 22 0.11700 7.1 3.9 6.6 23 0.07260 7.7 4.3 9.5 24 0.04120 7.4 6.0 10.9 25 0.25100 7.3 2.0 5.2 26 0.00002 7.6 7.8 20.7