# st: WG: interpretation of interactions with only one variable in log format

 From P K To statalist@hsphsun2.harvard.edu Subject st: WG: interpretation of interactions with only one variable in log format Date Thu, 4 Jun 2009 16:34:56 -0700 (PDT)

```Hi,

I have two questions concerning the interpretation of an OLS regression with interaction effects, while only ONE of the interaction terms is in log format.

1) I have different dummies in my regression, and I interact each dummy with a logged continuous variable. How do I have to interpret the results:
ex.

MODEL 1:  without interaction effects (dummies only):
dummy 1 = -10
dummy 2 = -1.16
dummy 3 = 21

MODEL 2: with interaction effects:
dummy 1 & log(var1) = -18.49
dummy 2 & log(var1) = -28.98
dummy 3 & log(var1) = 43.83

How do I have to interpret the results of MODEL 2, in comparison to MODEL 1?
=> e.g. a 10% change in dummy1*log(var1) leads to a change in the dependent variable of -18.40*log(1.1) = -0.76, which is much weaker than
dummy 1 effect alone (-10) => interaction term weakens effect of dummy 1 on dependent variable?

2) I run the same models with a continuous variable instead of all dummies.

MODEL 1:  without interaction effects (continuous predictor variable only):
independent variable = -3.0

MODEL 2: with interaction effects:
independent variable * log(var1) = -4.78

How do I have to interpret the results of MODEL 2, in comparison to MODEL 1?
=> e.g., a 10% change in independent variable * log(var1) would lead to a change in the dependent variable of -4.78*log(1.1)=-1.978?
=> This does, however, not take into account that the independent variable hasn't been in log format. Should I rather use log(independent variable) for MODEL 1 and MODEL 2 and then compare the 2 models?

Thanks,
Pat

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