Linear Rescaling to Accurately Interpret Logarithms

Nick Huntington-Klein

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arXiv · 2106.03070

Linear Rescaling to Accurately Interpret Logarithms

Nick Huntington-Klein

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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 $\log_{1+p}(X)$ 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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BibTeX RIS

Nick Huntington-Klein. 2021-06-06. Linear Rescaling to Accurately Interpret Logarithms. https://arxiv.org/abs/2106.03070

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