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I am dealing with a regression model where both the DV and IV are log-transformed.

I have found this explanation of how to interpret the effects (both in the Cross-Validated hyperlink and in documents from ULCA and Cornell stats outreach);

Specifically;

Example D: Outcome transformed and exposure transformed

log(DV) = Intercept + B1 * log(IV) + Error 

"One percent increase in IV is associated with a (B1) percent increase in DV."

In my regression the IV is a continuous variable; date each year that an event occurred (e.g., julian date 130).

Let's say my B1 coefficient is 0.5. I'd say a 1% increase in the IV is associated with a 0.5% increase in the DV.

So what is a 1% increase in date? Is that a 1% increase in the mean date? For example if mean date was 130, a 10% increase would be the event occuring on 143, and would result in 5% increase in DV?

What if I had centered date, and now mean date = 0. B1 from the regression is still = 0.5, but obviously it doesn't make sense to now have a 10% increase in mean =0. The use of centered, anomaly type data is common in my field so the example isn't overly contrived.

How can I interpret this effect?

What seems most intuitive to me would be the percent change as a percent of the range of the IV...For example if the range of the IV was 30 days, a 10% change would be 3 days, irrespective of what the absolute mean value is.

Does that make any sense?

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  • $\begingroup$ When you graph a line and somebody says its slope is $0.5$, what does that mean to you? $\endgroup$ – whuber Feb 23 '15 at 23:57
  • $\begingroup$ You have a model in log(date)?? Is it meaningful to take logs of something with an arbitrary origin? If your IV is itself uninterpretable, you have a more basic problem than interpreting the coefficient. $\endgroup$ – Glen_b Feb 24 '15 at 0:21
  • $\begingroup$ @whuber, one unit increase in X, leads to 0.5 unit increase in Y; or log(date)*0.5. It seemed odd to me that with the percent change interpretation in a log-log regression, a one % change in the IV would depend on the mean, where as the coefficient does not change with the mean. I must not be understanding something here. $\endgroup$ – Dave M Feb 24 '15 at 13:24
  • $\begingroup$ @Glen_b, I don't completely follow. If an untransformed variable's coefficient has a clear interpretation, why would log-transforming make it uninterpretable? $\endgroup$ – Dave M Feb 24 '15 at 14:57
  • $\begingroup$ When you have variables with arbitrary origins, concepts like "percentage change" don't carry useful meaning. If the origin is arbitrary, the results of your analysis should not depend on where you put the origin (it shouldn't matter if I make tomorrow 'day 1' or Jan 1 44 BC 'day 1'. Either choice should give the same information. That doesn't happen with logs ... or to put it another way, you can't meaningfully take logs of a quantity whose origin is arbitrary. I can meaningfully take log of temp in Kelvin, but I can't take log of temp in Celcius or Farenheit. $\endgroup$ – Glen_b Feb 24 '15 at 23:04

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