The following data were collected on specific gravity and spectrophotometer analysis for 26 mixtures of NG (nitroglycerine),

Question:

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

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There is a need to estimate activity coefficients from the model
\[
y=\frac{1}{\beta_{1} x_{1}+\beta_{1} x_{2}+\beta_{3} x_{3}}+\varepsilon
\]
The quantity parameters \(\beta_{1}, \beta_{2}\), and \(\beta_{3}\) 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.