# Study on the Influence of Consumers' Purchase Intention of Selenium-Rich Agricultural Products
## 4 Logistic Regression Algorithm  
A logistic regression model is a probabilistic nonlinear regression model, and also an analysis method of multivariable relationships [44]. It is intended to explain the relationship between classification results, that is, dependent variable \(p\), and multiple influencing factors, that is, independent variable x. The basic principle of logistic regression analysis is to use a set of data to fit the logistic regression model, which is used to reveal the relationship between a number of independent variables x and a dependent variable \(p\) value, reflecting interdependence between \(p\) and x. A logistic regression model can effectively limit the range of dependent variables to [0, 1], so it is particularly suitable for studies where the dependent variable is a binary variable. In the study conducted in this paper, the dependent variable of consumers' willingness to buy selenium-rich agricultural products is \"yes\" or \"no\", and number is \"0\" or \"1\", so this paper intends to use a logistic regression model for analysis. Logistic regression analysis model is:  
\[p=f\left(\beta_{0}+\sum\limits_{i=1}^{n}\beta_{i}x_{i}\right)=\frac{1}{1+\exp -\left(\beta_{0}+\sum\limits_{i=1}^{n}\beta_{i}x_{i}\right)}=\frac{\exp\left( \beta_{0}+\sum\limits_{i=1}^{n}\beta_{i}x_{i}\right)}{1-\exp\left(\beta_{0}+ \sum\limits_{i=1}^{n}\beta_{i}x_{i}\right)} \tag{1}\]  
After transforming Equation (1), Equation (2) is obtained:  
\[Ln\left(\frac{p}{1-p}\right)=\beta_{0}+\sum\limits_{i=1}^{n}\beta_{i}x_{i} \tag{2}\]  
Empirical model of consumers' willingness to purchase organic agricultural products: \(Y=F(X_{1},X_{2},X_{3},X_{4})\). Among them, \(Y\) is consumer's willingness to purchase selenium-rich agricultural products. In this model, there are four factors that affect consumer's willingness to purchase selenium-rich agricultural products: \(X_{1}\) is consumer's personal and family factors, \(X_{2}\) is consumer's attitude towards selenium-rich agricultural products and risk perception factors, \(X_{3}\) is consumer's health and environmental protection motivation factors, and \(X_{4}\) is product and market factors of selenium-rich agricultural products. Each aspect of factors is reflected by several specific variables. There are 22 such variables, and results of these 22 variables are all from the questionnaire. Figure 9: Technical Roadmap. \(Y=0\) means consumers have no intention to purchase selenium-rich agricultural products, and \(Y=1\) means consumers have intention to purchase selenium-rich agricultural products. \[X_{1}=f(x_{1},x_{2},x_{3},x_{4},x_{5},x_{6},x_{7},x_{8}) \tag{3}\]  
In above formula, \(x_{1}\) represents gender of consumer, \(x_{2}\) represents age of consumer, \(x_{3}\) represents education level of consumer, \(x_{4}\) represents marital status of consumer, \(x_{5}\) represents occupation of consumer, \(x_{6}\) represents family size of consumer, \(x_{7}\) represents whether there are elderly or children in family structure of consumer, and \(x_{8}\) represents monthly family income of consumer. \[X_{2}=f(x_{9},x_{10},x_{11},x_{12}) \tag{4}\]  
In above formula, \(x_{9}\) represents understanding degree of selenium-rich agricultural products, \(x_{10}\) represents trust degree of selenium-rich agricultural products, \(x_{11}\) represents evaluation degree of selenium-rich agricultural products, and \(x_{12}\) represents risk awareness degree of food safety. \[X_{3}=f(x_{13},x_{14}) \tag{5}\]  
In above formula, \(x_{13}\) represents degree of consumers' concern for environmental protection, and \(x_{14}\) represents degree of consumers' concern for health.