# Don’t Sleep on the Interaction Term

The majority of the traffic to this blog comes from the United States, but there’s a fair amount from other countries, pretty widely distributed.

I figured you could predict the traffic (excluding the United States) fairly well from the number of English speakers and the GDP per capita of the country, but a simple regression on these two variables doesn’t do a very good job:

On the other hand, if you include an interaction term (ie, you’re regressing on GDP per capita, the number of English speakers in the country, and GDP times number of English speakers), it does a much better job, explaining about 75 percent of the variation (the United States ends up being more-or-less right on the line, but it’s so far above everything else in both predicted and actual score that the graph becomes totally unreadable if you include it):

Interaction terms– they explain a lot.

## 5 thoughts on “Don’t Sleep on the Interaction Term”

1. Try plotting with log-log axes. Also, did you calculate “percent variance explained’ on relative or absolute variance? If the latter, the few biggest points might dominate the estimate.

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1. Yeah, there’s definitely a leverage issue there- that’s obvious if you include the United States, where suddenly 96% of the variation is explained. Good thoughts!

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2. The actual direct effects not being significant but the interaction is actually is a good clue that you should be using logs.

E.g. if you have something like:

y = 0*GDP + 0*E + 1*(GDP*E)

it suggests that

y = ?*log(GDP) + ?*log(E)

might be a better fit in many situations, since log(GDP*E) = log(GDP) + log(E).

(Unless you have some real substantive *apriori* reason why the first model is correct. It is weird in most situations though to have a higher order interaction, but not a direct effect.)

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1. The direct coefficients are still significant when you include the interaction, but they actually become negative. But your argument still makes sense.

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