An article in the Journal of Pharmaceuticals Sciences (1991, Vol. 80, pp. 971€“977) presented 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 Table 6E.8, where y is the negative logarithm of the mole fraction solubility, x₁is the dispersion partial solubility, x₂is the dipolar partial solubility, and x₃is the hydrogen bonding partial solubility.

(a) Construct a matrix of scatter plots for these variables.

(b) Comment on the apparent relationships among y and the other three variables?

Table 6E.8 

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Observation Number 0.0 1 0.22200 7.3 0.0 0.39500 2 8.7 0.0 0.3 0.7 3 0.42200 8.8 1.0 0.2 0.43700 8.1 4.0 5 0.42800 9.0 0.5 1.0 6. 0.46700 8.7 1.5 2.8 0.44400 9.3 2.1 1.0 8. 0.37800 7.6 5.1 3.4 0.49400 10.0 0.0 0.3 8.4 4.1 10 0.45600 3.7 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 7.3 14 0.10100 2.5 6.8 15 0.23200 8.5 2.0 6.6 0.30600 16 9.5 2.5 5.0 2.8 17 0.09230 7.4 7.8 18 0.11600 7.8 2.8 7.7 19 0.07640 7.7 3.0 8.0 10.3 4.2 20 0.43900 1.7 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 7.4 10.9 24 0.04120 6.0 25 0.25100 7.3 2.0 5.2 26 0.00002 7.6 7.8 20.7