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# st: Interpretation of interaction with dummy in OLS

 From P K To statalist@hsphsun2.harvard.edu Subject st: Interpretation of interaction with dummy in OLS Date Fri, 27 Aug 2010 19:48:46 +0000 (GMT)

```Dear Statalist,

I have several questions on how to interpret the results of an OLS regression
with an interaction between a dummy and a logged independent variable.

I tested the model

Y = a + b_IV + c_D + d_IV*D + e

IV is log-transformed.
D is a dummy.
Y is not log-transformed.

Comparing the model without the interaction (i.e. Y = a + b_IV + c_D  + e) to
the model with interaction (Y = a + b_IV + c_D + d_IV*D + e) yields the

following results for the coefficients:

b changes from 5 (model without interaction) to -6 (not significant in both
models)
c changes from 12 (significant) to -12 (not significant in model with
interaction)
interaction coefficient for model with interaction is 42 and significant.

I have the following questions:
(1) Does the significant and positive interaction term imply that the effect of
the logged IV on Y is positive and significant when the dummy is 1?

(2) If I want to test whether the logged IV moderates the relationship between
the dummy and Y, is the following interpretation right?
- dummy c has positive and significant relation with Y
- logged IV positively moderates the relationship between dummy and Y
(interaction term positive and significant)?

(3) What are possible explanations for the dummy turning negative and
insignificant when the interaction with logged IV is entered? May it be that the

interaction  between dummy and logged IV, rathr than only the dummy, has a
relationship with Y?

(4) Is there any way to give an idea how large the moderation effect of dummy
and logged IV are on Y? (i.e. total effect = c+d  or  c+b+d?)

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```