Solved: An article in the Journal of Pharmaceuticals
Chapter 12, Problem 87E(choose chapter or problem)
An article in the Journal of Pharmaceuticals Sciences (1991, Vol. 80, 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 Table E12-13, where y is the negative logarithm of the mole fraction solubility, \(x_1\) is the dispersion partial solubility, \(x_2\) is the dipolar partial solubility, and \(x_3\) is the hydrogen-bonding partial solubility.
(a) Fit the model \(Y=\beta_0+\beta_1 x_1+\beta_2 x_2+\beta_3 x_3+\beta_{12} x_1 x_2+ \beta_{13} x_1 x_3+\beta_{23} x_2 x_3+\beta_{11} x_1^2+\beta_{22} x_2^2+\beta_{33} x_3^2+\epsilon\)
(b) Test for significance of regression using \(\alpha=0.05\).
(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 \(\alpha=0.05\).
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