变量自然对数转换的多重线性回归

Multiple linear regression models with natural logarithmic transformations of variables

一般情况下,数据自然对数转换可使变量满足线性回归的应用条件。本文从实际应用出发,介绍了在进行线性回归分析时,自变量自然对数转换、因变量自然对数转换和两者都进行自然对数转换后,不能直接用X和/或Y的改变量解释回归方程和系数的原因,并阐述了用X和/或Y的百分比改变来解释回归方程和系数的原理。最后,用三个实例演示自变量、因变量、两者都进行自然对数转换,对拟合线性回归的结果进行了详细解释。

In general,the application conditions of linear regression models could be met after the natural logarithmic transformation of data.From the practical perspective,this paper introduced the linear regression models with natural logarithmic transformation of independent variable,dependent variable,and both independent and dependent variables in detail.The paper illustrated why the equation and coefficients could not be directly explained after the natural logarithmic transformation of data.The percentage changes of X and/or Y were applied to elaborate the principle and method for the explanation of the equation and coefficients.Three examples were used to fit simple linear models with natural logarithmic transformation of independent,dependent,and both independent and dependent variables and the results of theses models were explained in detail.