# Should I use ANCOVA or multiple regression with dummy variables?

I am writing a manuscript using an experimental design which predicts interactions between 1 continuous variable and multiple dichotomous variables, all predicting a continuous variable. As is traditional in experimental design, I have used ANCOVAs to analyze the data, but am concerned about the inability to specifically test the interaction between the covariate and the dichotomous variables.

Also, while I am expecting only a small amount of variance to be explained, there is only one significant finding among the multiple predictors and interactions. I suspect the non-significant findings may be due to the small amount of explained variance in the DV, which when spread across multiple predictors in the model is insufficient to distinguish between them.

A colleague has suggested that the best option to deal with both concerns is to do four 2 or 3 stage hierarchical regressions with dummy variables, i.e. each regression would comprise: stage 1: one dummy variable stage 2: add the continuous variable and the interaction between the two. After running these analyses, any significant predictors and interactions could be combined into a single hierarchical regression.

I am unable to find a precedent for this unusual procedure but interestingly, it reveals a number of significant results, albeit explaining a very small amount of variance.

Is this a reasonable procedure to follow, given the requirements of my variables?

• Hi Camille, welcome to the site. Your question looks interesting, but you're probably more likely to get better answers if your provide some specific details of what you're looking at. See meta.stats.stackexchange.com/questions/1479/… Dec 10, 2012 at 10:03
• @naught101. Thanks for the direction. I thought it would be easier to answer if I wrote in abstract ideas rather than specific variables but here goes. I'm a statistician so just wrote Dec 10, 2012 at 11:04

ANCOVA and multiple regression are mathematically identical. In matrix algebra terms, both are $Y + XB + e$. If you don't have much variance explained in ANCOVA, you won't in regression.