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Regression vs. AOV: Which to Choose?

Sheinberg, Joshua
In this study, we explore the differences between two common statistical methods (Regression and Analysis of Variance) on predicting the average household adjusted income across the 50 states in 2015. These two methods will be compared in two different settings, each using two predictor variables; one with a significant interaction present between the two predictors and one without a significant interaction. These methods are compared from the context of the research question being considered, the statistical results, the graphical results, and the resultant answer (interpretation of the statistical and graphical results). In the end, we find that neither model is objectively better than the other. We do find, however, that the added complexity of Regression models does not always result in an answer that differs from the simpler AOV model when there is no interaction present. With an interaction, we find that AOV does not always tell the whole story.
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