Linear Rescaling to Accurately Interpret Logarithms

Nick Huntington-Klein

Papers from arXiv.org

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 \(\log(1+X)\).

Date: 2021-06, Revised 2021-10
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http://arxiv.org/pdf/2106.03070 Latest version (application/pdf)

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Journal Article: Linear Rescaling to Accurately Interpret Logarithms (2023)
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