Stability of Drugs and Dosage Forms Sumie Yoshioka

2.2. • Factors Affecting Chemical Stability 69
Figure 37. Arrhenius plot for the degradation of vitamin A obtained by a modified analysis according to Eq.
(2.75). The upper and lower curves represent 95% significance limits. (Reproduced from Ref. 314 with permission.)
least-squares regression analysis of the rate constant k T at a temperature T, this results in a
larger contribution from the data obtained at lower temperatures than from those obtained at
higher temperatures (Fig. 38). To avoid this problem, Bentley proposed a weighted least-squares
analysis in which the error term ε is added to k as described by Eq. (2.77) rather than Eq. (2.76).
(2.76)
(2.77)
Weighted least-squares analysis provides the variance of experimental errors on the basis of
which the linearity of the Arrhenius plots can be assessed.
2.2.4.2.b. Prediction of Degradation Rate by Nonlinear Regression Analysis of the
Arrhenius Equation. Although linear regression analysis provides biased results and
weighted least-squares analysis is required to improve the estimates, nonlinear regression
analysis does not suffer from the same problem. Representing Eq. (2.75) in a nonlinear
manner yields Eq. (2.78) for first-order degradation kinetics. 318 Similarly, Eq. (2.79) is
obtained for zero-order degradation kinetics.
(2.78)
(2.79)