## 2 Materials and Methods
### Statistical Model Development  
Mathematical and statistical methods were used in chemometrics to select the optimal experimental method and to analyze chemical data [33; 34]. This method is used in many different fields of study, including science and engineering, and has had a particular impact in the field of spectroscopy [34]. Chemometrics tools include multiple linear regression (MLR), principal component regression (PCR) [35; 36], and partial least squares (PLS) regression [37]. The main (multiple) linear calibration methods included: multiple linear regression (MLR), principal component regression (PCR), and partial least squares (PLS). MLR is a linear statistical technique for predicting a response (dependent variable) using two or more multiple predictors (independent variables). However, when MLR is used, a multilinear phenomenon may occur. In a multilinear model, a predictor variable in an MLR model can be linearly predicted with considerable accuracy [38]. Therefore, the estimate of MLR coefficients may change irregularly due to small changes in the model or data. PCR is a multilinear problem solution based on PCA. Under this regression model, a set of predictors is considered based on a standard linear regression model, but PCA is used to estimate the unknown regression coefficients in the model. PCR, a method based on dimensionality reduction, selects some principal components with high variance in the regression phase, which leads to dimensionality reduction by reducing a sufficient number of parameters to describe the base model [39]. In addition, PLS regression is a reliable and effective multivariate chemometric method that is often used to develop a mathematical model between spectral data and reference measurements [40]. [PERSON] [34] proposed this linear statistical method, which is often referred to as component-based structural equation modeling. PLS variables are different from other methods, such as PCA, which looks for maximum variance schemes between output and input variables. PLS variables show output and input in a new space and then find a linear regression method in the predicted space. It is also a non-parametric method that does not require data normalization and is strong to sample size [41].  
The main difference between PLS and PCR is that the latter considers only the X-variable matrix, while PLS includes the Y-response matrix in the regression phase [34]. Multivariate calibration, PLS, PCR, and multiple linear regression (MLR) have been used to predict the percentage of ternary mixtures of cattle, ewes, and goats based on the analysis of milk protein by capillary electrophoresis [42]. MLR and PLS calibration methods were previously used to determine the absorption signal of drugs during drug preparation [43]. Furthermore, PLS and PCR predictions of protein content and hardness for bulk Canadian wheat samples were compared using infrared and near-infrared imaging [44]. These analytical methods also were used to quantify sugar in acarbose fermentation using infrared spectroscopy and chemotherapy [45] and simultaneously evaluate different soil properties [46]. A quantitative PLS model was employed for determining water content of peanut kernels utilized hyperspectral imaging techniques [47].