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st: Question on interpreting interactions in linear regression models


From   Padmakumar Sivadasan <pmathru2@illinois.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: Question on interpreting interactions in linear regression models
Date   Tue, 15 Dec 2009 09:49:46 -0600

Hello,

This is a basic question about interpreting interactions in linear
regression models that I hope someone would be able answer or guide me
to a useful reference.

I was reading a paper in which the authors are interested in studying
whether the effect of a continuous variable (X) on a continuous
outcome variable (Y) varies between two periods (P=0 and P=1). They
test this using interactions with the following linear regression
model  Y=b1+b2X+b3P+b4XP

They find that b2 is significantly different from zero, while b4 and
(b2+b4) are not significantly different from zero. The authors
conclude that X has an influence on Y in the first period (i.e. when
P=0) because b2 is significant. Further, they state that the influence
of X in the second period (i.e. when P=1) is given by (b2+b4) and this
is not significantly different from zero, implying that X has no
influence on Y in the second period. Thus, the effect of X on Y varies
between the two periods.

Is this interpretation of the authors correct? Does not the fact that
the interaction coefficient (b4) is non-significant directly imply
that there is no change in the effect of X between the two periods?

Thanks

Padmakumar

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