When respecifying a categorical variable with K categories,only K - 1 dummy variables are needed because only K - 1 categories are independent.

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Quizplus · Accepted Answer

This is known as the "dummy variable trap" and is a consequence of linear dependencies that occur when using all K categories as predictors. One category must be excluded as a reference category to avoid perfect multicollinearity in the model.

When Respecifying a Categorical Variable with K Categories,only K -