Yesterday I gave a little quiz about interpreting regression coefficients. Today I’m giving you the answers.
If you want to try it yourself before you see the answers, go here. (It’s truly little, but if you’re like me, you just cannot resist testing yourself).
True or False?
1. When you add an interaction to a regression model, you can still evaluate the main effects of the terms that make up the interaction, just like in ANOVA.
In an ANOVA table (even the one in the regression output), categorical variables are Effect Coded. Because of that, the main effects remain main effects, and are evaluated independent of interactions.
But in the Regression Coefficients table, unless you are explicitly effect coding, they will be Dummy Coded. The coefficient for what looks like a main effect IS NOT a main effect. It’s a marginal effect–the effect of that predictor ONLY when the other predictor in the interaction =0! I kid you not.
2. The intercept is usually meaningless in a regression model.
This statement is only true if all predictors are continuous and the data don’t contain 0. If continuous predictors are centered and/or if there are dummy variables in the model, the intercept is meaningful and important.
3. In Analysis of Covariance, the covariate is a nuisance variable, and the real point of the analysis is to evaluate the means after controlling for the covariate.
It can be true, but it doesn’t have to be. Covariates are often important predictors that just happen to be observed and continuous. The only way to evaluate them is to examine their coefficients.
4. Standardized regression coefficients are meaningful for dummy-coded predictors.
This one is never ever true. Just because your software lets you get away with it doesn’t mean it’s meaningful.
5. The only way to evaluate an interaction between two independent variables is to categorize one or both of them.
Sure, it’s tricky to interpret interactions between two continuous variables, but by no means is it impossible or theoretically incorrect. (And centering really helps).
How did you do? (BTW, it took me years of figuring all this stuff out in a way that was really intuitive, even after many stats classes).