## 1 Introduction
For the fitting agreement, the criteria involve the F-value of ANOVA, coefficient of determination R\({}^{2}\), adjusted R\({}^{2}\)\(\mathrm{R}^{2}\)\(\mathrm{R}^{2}\)\(\mathrm{adj}\), lack-of-fit test, etc. The criteria to evaluate predictive ability are PRESS, predicted R-squared R\({}^{2}\)\(\mathrm{pred}\), and adequacy of precision. The VIF (variance inflation factor) is used to test the collinearity of these factors [1; 5; 11]. The \"Materials and Methods\" Section introduces the calculation equations and their meaning. After evaluating the adequacy of the equation (RSM model), the final model is called an adequate regression equation. Two methods are used to determine the optimization. The first one uses the first partial derivatives of the response in terms of each factor. For example, if three factors are considered, three gradient equations of this equation are derived, and the three optimum conditions are solved with these derivative functions [1]. The second method is the graphic method, which provides the figures observed by researchers. The contour and 3D response surface plots are popular among researchers [1; 3; 12; 13]. The investigated technique has been illustrated in detail [14]. Accuracy and validity are the keys to finding reliable results regarding the factors influencing the response. They involve the factors that affect the response and the degree to which these influencing factors influence. However, the adequacy of the regression equations is not of concern to researchers. Many researchers use commercial software directly. [PERSON] et al. [15] mention the importance of the model's validity and accuracy in their suggestions about the challenges associated with RSM application. The authors emphasized that the RSM model depends on the statistical technique and the importance of ensuring the accuracy and validity of the RSM model [15]. An excellent RSM textbook has been published [1]. [PERSON] and [PERSON] [2] provided an important concept of RSM. [PERSON] et al. [3] introduced the historical background of RSM. These papers involved science and technology, analytical methods, and process systems aplenty [16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27]. The topics of this literature included drying, extraction, fermentation, blending, mixing, and others [16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27]. The unique feature of response surface methodology is the graphical presentation of the relationship between the influential factors (variables) and the response. The contour plot represents the information in a two-dimensional form. The variation in the response under different conditions of influencing factors is indicated with the contour plot. The 3D response surface plot represents the information in three-dimensional form. The response is the z-coordinate, and the two influencing factors are the x- and y-coordinates. If a quadratic polynomial relationship does not exist, linear lines are plotted in this contour plot and a 3D response surface plot as the plateau. If the quadratic relationship is significant, two plots are presented with curves. The contour plot is usually used to observe visually the optimum levels of the influencing factors (the input variables) that can result in the maximum response [1; 2; 3]. The purpose of an RSM experiment in science and technology is to find the optimal conditions. If the RSM model is a linear equation, the contour plot and response surface plot indicate the response direction to the original design. Suppose that the RSM model is a quadratic equation. Both plots will indicate the maximum, minimum, or saddle conditions. Establishing an appropriate RSM equation is essential to ensure correct optimization conditions. The regression technique for RSM needs to be considered. In the classical regression equation, the least squares method establishes the equation, and the estimated values of the parameter coefficients are directly used.