How do I interpret an independent variable which is a log(%)?

Asked Aug 13 '23 at 15:08

Active Aug 13 '23 at 15:23

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My linear regression is:

School's average test score ~ log(%FSM)

%FSM = the percentage of pupils at the school who are eligible for free school meals (an indicator of low socio-economic status).

The coefficient for log(%FSM) is -10.

Do I interpret this as: a 1% increase in the %FSM pupils is associated with a decrease of 0.1 in average test score?

Or, because this is a log of a % is the interpretation different from the above? I think this is also a 1% increase, NOT a 1 percentage point increase. Is there a clearer way to make this distinction in my interpretation?

asked Aug 13 '23 at 15:08

Jess

This is a FAQ: please search our site for log regression dependent interpretation. – whuber Aug 13 '23 at 15:21
Hello, thank you for sharing the link, but I cannot find a post which specifically talks about the effect of a log % IV on a non-log DV. – Jess Aug 13 '23 at 16:28
We have a great many posts concerning all possible combinations of logs (and other transformations) on the DVs and the IVs. Here's a search. – whuber Aug 13 '23 at 16:28

How do I interpret an independent variable which is a log(%)?

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