Final answer:
The dummy variable trap is avoided by including one less dummy variable than the number of categories in a linear regression model with an intercept. This prevents multicollinearity and allows for proper estimation of regression coefficients, with the intercept representing the baseline category.
Step-by-step explanation:
The problem that is avoided by having one less dummy variable than the number of categories in a categorical variable when including an intercept in the linear regression model is known as the dummy variable trap. The dummy variable trap occurs when the dummy variables are multicollinear, meaning that one variable can be perfectly predicted from the others, leading to redundant information. In regression analysis, this can cause issues with the estimation of the regression coefficients. By using one less dummy variable, we prevent perfect multicollinearity, as the remaining dummy variables capture the differences between categories, and the intercept represents the baseline category.
In practice, if we have a categorical variable with three categories, A, B, and C, we would include two dummy variables in the model. For instance, if D1 represents category A (where D1 is 1 for category A and 0 otherwise) and D2 represents category B (where D2 is 1 for category B and 0 otherwise), category C would be the baseline and is represented when both D1 and D2 are 0.