where β0 is the intercept, βi, βii, βij, βiii, and βijk are the regression coefficients for linear, quadratic, and interaction terms, respectively, Xi, Xj, and Xk are the independent variables, and ϵ is the residual error. The adequacy of the model and significance of each linear, non-linear, and interactive term based on independent variables was assessed through analysis of variance (ANOVA), and coefficient of determination (R 2 ).