In a regression model’s formula, an interaction term captures an interplay between two predictor variables, which happens when the effect of one predictor variable on the response variable is modulated by the other predictor variable. An interaction term should be in a regression formula and the resulting model when a change in the estimated response due to the combination is more than the change due to each predictor alone.
Our data for U.S. states doesn’t appear to have variables that suggest an interaction, but if we knew which states had carried out death sentences in the past five years, or which states had three-strikes-and-you’re-out felony laws, it is possible that we would find an interaction term of either of those variables combined with the number of prisoners.
Among the tools that can help spot potential interaction terms, one is an interaction plot. Parallel lines in an interaction plot indicate no interaction. The greater the difference in slopes between the lines, therefore, the higher the degree of interaction.
One form of interaction plot would have an upper solid line that marks one standard deviation of the response variable (practicing lawyers at the top and a lightly dotted line that marks one standard deviation of those lawyers at the bottom. A dotted line midway would indicate the average number of lawyers. However, an interaction plot doesn’t say whether the interaction is statistically significant.