Experiment design and statistical analysis

In the determination of the optimum baking temperature and time, RSM was performed using the Design-Expert software version 10.0.3.1 (Stat-Ease Inc., Minneapolis, USA). A 2-variable, 3-coded level central composite design (CCD) was selected to accommodate the 13 experimental conditions (Gan et al. 2007). The independent variables were baking temperature (X₁; 150 °C, 160 °C, 170 °C) and time, X₂ (air fryer: 25, 30, 35 min; convection oven: 35, 40, 45 min). The experimental designs for the uncoded and coded values of the independent variables are shown in Table 1. The dependent values included the relative central height of the cake, moisture content, and texture characteristics. The regression coefficients of the individual linear, quadratic and interaction terms were determined using a second-order polynomial by the following equation:

The coefficients of the polynomial were represented by: Y, desired value of response (relative central height, crumb moisture content and firmness, chewiness and springiness); b_o, intercept; b₁, coefficient for baking temperature (first order); b₂, coefficient for baking time (first order); b₁², coefficient for interaction between baking temperature and time; b₃², coefficient for baking temperature (second order); b₄², coefficient for baking time (second order); X₁, baking temperature (°C); X₂, baking time (min).

Experimental data on the responses of optimization baking parameters for moist chocolate cake baked using air fryer and convection oven

^aCoded value

^bX₁ = baking temperature (°C), X₂ = baking time (min)

^cY_1,6 = relative height (%), Y_2,7 = moisture content (%),Y_3,8 = firmness (N), Y_4,9 = chewiness (N), Y_5,10 = springiness (%),Y_6,11 = color change (ΔE)

The RSM also was used to perform the analysis of variance (ANOVA). The value of significance was set at 5%. The regression coefficient was used in the statistical calculation to generate a contour map based on the regression models.