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I have more of a theoretical question regarding the use of dummy regression. I know that one level of a categorical variable is used as a reference group, and the means of all subsequent levels are compared to the mean of the reference group, and that these differences give different p-values.

I understand how each level in a categorical variable is interpreted for a categorical variable, but I am not sure how the p-value in the reference group should be interpreted. This may be too simplistic, but I thought the interpretation of a reference group was not meaningful because I believe the mean is being compared with itself, and thus not useful. Is this an inappropriate way of conceptually understanding my question?

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You can think of the coefficient for the reference group as comparing the reference group mean to 0. So the t-statistic and p-value for that coefficient reflect the null hypothesis that the mean of the reference group = 0.

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