灰色GM(1,1)模型与线性回归模型的内在联系

The Internal Connection between Grey GM(1,1) Model and Simple Linear Regression Model

摘要: 目的：对经过平移变换后的原始序列建立GM(1,1)模型，其模拟序列与一元线性回归直线非常相似，为此探究两种模型间的联系。方法：在真实世界中取多组原始序列，进行平移变换后构建GM(1,1)模型，再与一元线性回归模型进行比较，使用T检验和差异度量方法对结果进行量化。结果：去掉原始序列第一个数据后用其余数据建立的一元线性回归模型和经过较大平移变换后基于全部原始序列建立的GM(1,1)模型相同。结论：经过平移变换后，灰色模型表现为一种特殊的线性回归模型。

Abstract: Purpose: The analog sequence of GM(1,1) model for the original sequence after translation trans-formation, is very similar to simple linear regression line. So, we will explore the relationship be-tween the two models. Method: Get some original sequences from real world, construct GM(1,1) model after translation transformation and simple linear regression model, and use T test and difference measure to compare the two models. Result: The GM(1,1) model constructed by the original sequence after translation transformation, and the simple linear regression model constructed by the sequence except the first data, are the same. Conclusion: After translation transformation, the grey model becomes a special linear regression model.