Final answer:
The statement that perfect collinearity occurs during the dummy variable trap, causing a regression model to crash is true. To prevent this, typically one dummy variable category is omitted to preserve independence among the variables.
Step-by-step explanation:
The statement 'When the dummy variable trap occurs, there is PERFECT COLLINEARITY and the regression will crash' is True.
The dummy variable trap is a scenario in which two or more dummy variables created in a regression model are highly correlated (multicollinear), leading to redundancy. This occurs when the dummy variables are not independent from one another, often because one dummy variable can be predicted from the others.
For example, if we have a model with three categories where we create three dummy variables (one for each category), the third dummy can be perfectly predicted by the first two, resulting in perfect collinearity.
This perfect collinearity can invalidate the regression model as it makes it impossible to estimate unique effects of the dummy variables on the dependent variable.
In regression analysis, to avoid the dummy variable trap, one category is usually omitted from the regression model, creating a baseline against which the impact of other categories is measured. This ensures the independence of the dummy variables and allows the regression to produce meaningful results.