[Multiple linear regression models with natural logarithmic transformations of variables]

Area of Science:

• Statistics
• Econometrics

Background:

• Linear regression models are widely used but often require data transformation to meet assumptions.
• Natural logarithmic transformation is a common technique to stabilize variance and linearize relationships.

Purpose of the Study:

• To detail linear regression models incorporating natural logarithmic transformations of independent variables, dependent variables, or both.
• To clarify the interpretation of coefficients and equations after logarithmic transformation.
• To provide practical guidance on explaining model results using percentage changes.

Main Methods:

• Introduction of linear regression models with natural logarithmic transformation applied to X, Y, or both.
• Explanation of why direct interpretation of coefficients is not feasible post-transformation.
• Application of percentage changes in X and/or Y to interpret model parameters.

Main Results:

• Demonstration of how logarithmic transformations can satisfy linear regression assumptions.
• Development of a method to interpret coefficients in terms of percentage changes.
• Illustration through three examples of fitting and interpreting transformed linear models.

Conclusions:

• Natural logarithmic transformation is a viable method for applying linear regression models.
• Percentage change interpretation is crucial for understanding the practical implications of transformed models.
• This approach enhances the applicability and interpretability of regression analysis in various fields.