Final answer:
When including dummy variables for each category in a model, the sum of those dummy variables will equal one for any given observation due to how dummy variables are assigned to represent categories in statistical models.
Step-by-step explanation:
If we include as many dummy variables as there are categories, then their sum will equal one for any given observation. This is because dummy variables are used in statistical modeling to represent categorical data, particularly in regression models. Each category is assigned a dummy variable (except for one reference category), where the value is 1 if the observation belongs to that category and 0 otherwise.
Thus, if you have created dummy variables for each category, only one of these dummy variables can take the value of 1 for a given observation (indicating the category that the observation falls into), while the others would be 0. This is also known as the dummy variable trap. To avoid this, one category is typically left out as the base or reference group. This is not just a practical approach to avoid multicollinearity but a necessary condition for the model to be properly specified.