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.