**5. Model development**

A model is an expression that shows how quantitatively dependent the independent variables are on a response variable. Both theoretical and empirical numerical models are possible. A way to explain the relationship between factors and responses is through an empirical model. It is typically a collection of polynomials of a certain order or degree. First, second, and sporadically third order polynomials are the models most frequently used to describe the response(s). The initial hypothesis is a first order model. Higher order models are used if a simple model is found to be insufficient for explaining the phenomenon.

Using regression analysis, the coefficients for quantitative factors can be estimated. Regression analysis is not used in the case of qualitative factors, however, because interpolation between discrete (i.e., categorical) factor values is meaningless. Multiple linear regression analysis (MLRA) is typically preferred for situations where there are more factors, interactions, and higher order terms. When the factorresponse relationship is nonlinear, multiple nonlinear regression analysis is advised. The techniques of partial least squares (PLS) or principal component analysis can also be used for regression in multivariate studies where there are numerous variables [21]. When there are fewer observations than there are predictor variables, PLS, an extension of MLRA, is used. ANOVA, Student's t test [22], predicted residual sum of squares, and Pearsonian coefficient of determination When there are fewer observations than there are predictor variables, PLS, an extension of MLRA, is used. ANOVA, Student's t test [22], predicted residual sum of squares, and Pearsonian coefficient of determination are all taken into account when conducting model analysis (r2) are all taken into account when conducting model analysis. The essential stages required in developing and examining a mathematical model is outlined in the narrative that follows [23]:


• The model's findings are used to determine critical elements, identify ideal conditions, and other things.
