Linear Rescaling to Accurately Interpret Logarithms
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Nick Huntington-Klein
Abstract
The standard approximation of a natural logarithm in statistical analysis interprets a linear change of p in ln(X) as a (1 + p) proportional change in X, which is only accurate for small values of p. I suggest base-(1 + p) logarithms, where p is chosen ahead of time. A one-unit change in log1 + p(X) is exactly equivalent to a (1 + p) proportional change in X. This avoids an approximation applied too broadly, makes exact interpretation easier and less error-prone, improves approximation quality when approximations are used, makes the change of interest a one-log-unit change like other regression variables, and reduces error from the use of log(1 + X).
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Articles in the same Issue
- Frontmatter
- Research Articles
- Empirical Framework for Two-Player Repeated Games with Random States
- The Robustness of Conditional Logit for Binary Response Panel Data Models with Serial Correlation
- Density Forecast of Financial Returns Using Decomposition and Maximum Entropy
- On the Implementation of Approximate Randomization Tests in Linear Models with a Small Number of Clusters
- Quantile Difference in Differences with Time-Varying Qualification in Panel Data
- A Random Forest-based Approach to Combining and Ranking Seasonality Tests
- Teaching Corner
- On the Use of the Helmert Transformation, and its Applications in Panel Data Econometrics
- Practitioner's Corner
- Linear Rescaling to Accurately Interpret Logarithms
Articles in the same Issue
- Frontmatter
- Research Articles
- Empirical Framework for Two-Player Repeated Games with Random States
- The Robustness of Conditional Logit for Binary Response Panel Data Models with Serial Correlation
- Density Forecast of Financial Returns Using Decomposition and Maximum Entropy
- On the Implementation of Approximate Randomization Tests in Linear Models with a Small Number of Clusters
- Quantile Difference in Differences with Time-Varying Qualification in Panel Data
- A Random Forest-based Approach to Combining and Ranking Seasonality Tests
- Teaching Corner
- On the Use of the Helmert Transformation, and its Applications in Panel Data Econometrics
- Practitioner's Corner
- Linear Rescaling to Accurately Interpret Logarithms
