多项式回归与响应面分析的原理及应用

Principle and Application of Polynomial Regression and Response Surface Analysis

相较于客观测量一致性研究问题的差异分数方法,多项式回归与响应面分析能更为深入地探究两个变量间的复杂关系。基于比较视角,文章阐述了如何正确地检验两个变量的一致性程度、同方向变化和反方向变化三种情形对结果变量的影响,并扼要分析其检验逻辑的合理性。此外,还重点探讨了如何检验有调节变量的和有中介变量的多项式回归,同时运用一个实例演示如何分析和汇报数据结果,并指出了运用多项式回归与响应面分析进行实证研究可能的发展方向。

Compared with the difference score method of measuring congruence research objectively,polynomial regression and response surface analysis can provide a deeper exploration on the complicated relationship between the two variables.Based on the comparative perspective,this paper expounds how to correctly test the effect of the congruence degree of the two variables,the change in the same direction and that in the opposite direction on the result variables,and then briefly analyzes the rationality of the testing logic.In addition,the paper focuses on how to test polynomial regression with moderating variables and with mediating variables,and also uses an example to demonstrate how to analyze and report data results.Finally,the paper points out the possible development direction of empirical research using polynomial regression and response surface analysis.