[R] Interpreting the coefficient of an interaction between continuous variables in a regression model

Sverre Stausland johnsen at fas.harvard.edu
Thu Mar 3 20:56:50 CET 2011


my question is triggered by an actual model I am running, but I will
pose it as a very general question with a hypothetical example.

Take the following regression model:

I have a binomial dependent variable "Happiness", whose two values are
0 (=unhappy) and 1 (=happy). My two independent continuous variables
are "Income" and "Children". Imagine that "Income" has no significant
effect, and that "Children" has a significant positive effect (more
children give more happiness). Now I am interested in the interaction
between "Income" and "Children", i.e. 'Income : Children'. Say that
the model finds a non-significant negative coefficient. How do I
interpret that? If I understand it correctly, the model is asking
"When the numerical values in "Income" and "Children" are both
increasing, does it significantly affect the dependent variable?". But
what if the interaction between them is inverse - such that a
decreasing value in "Income" paired with an increasing value in
"Children" will significantly affect the dependent variable
"Happiness". Will the model not be able to capture that connection
without doing some additional tweaking?

Thank you

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