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What method does mathematical modeling use to find out the mathematical function relationship between several variables from a large number of data?
Regression analysis can!

The so-called regression analysis method is to establish the expression of regression function between dependent variable and independent variable (called regression equation) by using the method of mathematical statistics on the basis of mastering a large number of observation data. In regression analysis, when the causal relationship only involves the dependent variable and an independent variable, it is called unary regression analysis; When the causal relationship studied involves dependent variables and two or more independent variables, it is called multiple regression analysis. In addition, regression analysis is divided into linear regression analysis and nonlinear regression analysis according to whether the functional expression describing the causal relationship between independent variables and dependent variables is linear or nonlinear. Linear regression analysis is usually the most basic analysis method, and nonlinear regression problems can be transformed into linear regression problems by mathematical means.

For details, please refer to the books on statistical regression.