CI, Confidence Interval; VIF, Variance Inflation Factor; df,
Degree of Freedom
Proper evaluation of experimental data consists of using statistical
methods and tools that offer freedom to evaluate complex hypothesis
(Deluba and Olive, 1996). In this study, regression analysis and
multivariate statistics were applied to describe the effects of
variables on the yield of tocopherol. As already known, water weight
(A), lipase weight (B) and reaction time (C) were the selected
independent variables, hence depicting a multivariate system in which
multivariate multiple regression analyses (results shown in Tables 3.5
and 3.6) were applied to predict the statistical relationship between
the response variable (total tocopherol, as vitamin E). The response
surface model has been developed to have the coexistence of both the
interacting and non-interacting model variables along with their
respective coefficients. Considering the results from both Tables 3.5
and 3.6, coefficients of model terms were estimated and summarized in
Table 3.7 in terms of confidence interval, degree of freedom, and
variance inflation factor. Therefore, the final equation in terms of
coded factors is as follows:
Total Tocopherol (as Vit. E) =\(\mathbf{6.42+0.36}\mathbf{A+0.58}\mathbf{B+0.83}\mathbf{C+0.059}\mathbf{AB+0.034}\mathbf{\text{AC}}\)
\(\mathbf{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ +0.63}\mathbf{BC+0.80}\mathbf{A}^{\mathbf{2}}\mathbf{-0.55}\mathbf{B}^{\mathbf{2}}\mathbf{-0.54}\mathbf{C}^{\mathbf{2}}\)(3.1)
The equation in terms of coded factors could be used to make predictions
about the response for given levels for each factor. High levels were
coded as +1 and the low levels of the factors were coded as -1. The
coded equation was useful for identifying the relative impact of the
factors by comparing the factor coefficients. Furthermore, in Eqs.
3.1, the coefficients were scaled to accommodate the units of
each factor and the intercept was not at the centre of the design space.