# Interpreting coefficient of a logarithmic coefficient in a logistic regression

I have a regression with a log-transformed independent variable, and I would like to know the proper way to explain its effect on my binary dependent variable.

For example, say the equation is:

(binary_variable)i = b0 + -0.03(log_variable)i

Does a 1% increase in log_variable mean a 0.03% (or 0.0003%?) reduction in binary_variable?

Thanks

• Are you using natural log (base e) or log base 10? – James Phillips Mar 22 at 18:52
• @jamesPhillips I believe I'm using natural log, per np.log (see docs.scipy.org/doc/numpy/reference/generated/numpy.log.html) – Nick Wishengrad Mar 22 at 20:18
• I would say that an increase in 1% in the log_variable results in the odds of the binary_variable being multiplied by $e^{-0.03 \times 0.01} \approx 0.9997$, i.e., a 0.03% decrease in the odds. – Ertxiem Mar 23 at 15:53