An article in the journal of pharmaceutical sciences (80, 971-977, 1991) presents data on the observed mole fraction solubility of a solute at a constant temperature, along with x1 = dispersion partial solubility, x2 = dipolar partial solubility, and x3 = hydrogen bonding hansen partial solubility. the response y is the negative logarithm of the mole fraction solubility.
(a) fit a complete second order model to the data.
(b) test for the overall significance of the regression.
(c) examine the residual plots and comment on the model adequacy.
(d) report r2 and r2adj. which gives a better assessment of the models predictive ability?
(e) test whether the second order terms are significant to the regression.
y x1 x2 x3
0.222 7.3 0 0
0.395 8.7 0 0.3
0.422 8.8 0.7 1
0.437 8.1 4 0.2
0.428 9 0.5 1
0.467 8.7 1.5 2.8
0.444 9.3 2.1 1
0.378 7.6 5.1 3.4
0.494 10 0 0.3
0.456 8.4 3.7 4.1
0.452 9.3 3.6 2
0.112 7.7 2.8 7.1
0.432 9.8 4.2 2
0.101 7.3 2.5 6.8
0.232 8.5 2 6.6
0.306 9.5 2.5 5
0.0923 7.4 2.8 7.8
0.116 7.8 2.8 7.7
0.0764 7.7 3 8
0.439 10.3 1.7 4.2
0.0944 7.8 3.3 8.5
0.117 7.1 3.9 6.6
0.0726 7.7 4.3 9.5
0.0412 7.4 6 10.9
0.251 7.3 2 5.2
0.2 7.6 7.8 20.7