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So normally I see dummy variables used when there are 2 options (e.g. a female dummy = 1 when the person is female, 0 if male).

However, what if I want to use a dummy variable to represent e.g. company size (i.e. small, medium and large)?

Would I need 3 dummies, i.e. small, medium and large, which each equal one if the company in the dataset is that size and 0 if not?

If so, how would I interpret the coefficient after a regression has been estimated? Because if e.g. small is a dummy and it equals 0, it doesn't mean that the company is e.g. medium-sized, since it could be large-sized.

Clarification appreciated!

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You could code them as 3-d vectors with a $1$ in the position corresponding to the category and $0$ in the other two positions. But...

...that's not how people tend to do it.

Usually people would make them 2-d vectors, where the first position is an indicator for being a medium company and the second position is an indicator for being a large company. Double $0$s would indicate that it is neither, which means that the category must be the remaining category: small company.

I wrote a post about how this work in ANOVA that I will link here in a moment.

https://stats.stackexchange.com/a/439818/247274

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