I have used simple linear regression, and I'm now checking that the model meets the assumption of linearity. The model used a continuous response variable and categorical explanatory variables. How can I asses linearity when using categorical explanatory variables?

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    $\begingroup$ If you have a single categorical variable you are effectively doing a one-way anova and the concept of a linear relationship between your regressors and your response isn't well defined since you don't have any way to measure the distance between your categories or for that matter even ordination. $\endgroup$ – Jonathan Lisic Jul 31 '12 at 19:42

Linear regression with only categorical explanatory variables is really ANOVA. With only one categorical predictor (with two or more levels) this is one-way ANOVA. In one-way ANOVA the linearity assumption is essentially empty, so there is nothing to check.

With two or more categorical predictors this corresponds to rwo-way (or higher) ANOVA. In this case also, linearity is empty, so there is nothing to check about linearity, but the question of including (or not) interactions arises, so should be checked/thought about.

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