With and Without You
No this isn’t some sappy ballad, though I’ve been meaning to write one of those. I was a musician way before I was a statistician. But now, I have a similar passion for both.
Lately, I have been tutoring a college student in econometrics. Her assignments require her to analyze statistical concepts and simulate them in STATA and R. The other day, she asked me about interpreting interactions in her regressions. Isn’t it a bit redundant to include a female term, a place of residence term and a female*place of residence term?
Not exactly. And here’s why:
Each term has its own impact on the dependent variable. The interaction is their combined impact.
Still confused? I don’t blame you. So think of it this way: If you are testing the impact of a variety of factors on TV show usage, you already know that some factors will be deemed as significant in the regression results and some will not. But often, it is not enough to test the significance of each variable on its own.
To illustrate this concept, a simple built-into-R dataset like mtcars works best, given that it’s made fully of numeric variables. My first regression was a simple test of number of the impact of weight (wt) and number of cylinders (cyl) on fuel efficiency (mpg). These were the results:
As you can see, based on the t-stats and p-values, weight has a significant impact on fuel efficiency and the other variables appear not to. But I’m not completely convinced. Some of these variables might be seemingly insignificant on their own, but when combined in tandem, may have impact.
It looks like I was right! The second model I did is a better fit according to the R-squared in both models. What do we notice? Weight and the number of cylinders are still both significant individually, but together, they are also significant. And after adding their conjoined impact, the model as a whole is improved by 3%.
Sometimes when statistical concepts go over my head, I try to relate them to situations we experience daily.
How different are these interactions between variables from our own personal interactions? Not very if you ask me. We make our own impacts on others as individuals. But what about when we join together? Couples become their own entities over time. Friends tackle parties together. And groups of people bonded around a common goal make the loudest difference. Sometimes the impact we can make on our own is not enough to reach a passionate goal, but in tandem with someone else’s, it becomes so. Just something to think about :)
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