3.19 The following data were collected on specific gravity and spectrophotometer analysis for 26 mixtures of NG (nitroglycerine), TA (triacetin), and 2 NDPA (2-nitrodiphenylamine).

Mixture 16 17 18 19 20 21 22 23 24 25 26 JCI (% NG) 69.98 69.98 69.99 69.99 67.51 67.50 67.48 67.49 64.98 64.98 64.99 x2 (% TA) 29.99 29.00 27.99 26.99 32.47 31.47 30.50 29.49 34.00 33.00 31.99 x3 (% 2 NDPA) 0 1.00 2.00 3.00 0 1.00 2.00 3.00 1.00 2.00 3.00 y (Specific Gravity) 1.4279 1.4287 1.4291 1.4301 1.4157 1.4172 1.4183 1.4188 1.4042 1.4060 1.4068 Source: Raymond H. Myers, Technometrics, vol. 6, no. 4 (November 1964): 343-356. There is a need to estimate activity coefficients from the model 1 y ~ ßxX\+ßxX2 + ß*x* + £ The quantity parameters ßu β2, and β3 are ratios of activity coefficients to the individual specific gravity of the NG, TA, and 2 NDPA, respectively.

(a) Determine starting values for the model parameters.

(b) Use nonlinear regression to fit the model.

(c) Investigate the adequacy of the nonlinear model.