The dummy variable trap is an example of:

Question

BlackTom AI · Accepted Answer

Perfect multicollinearity is present when one regressor can be expressed exactly as a linear combination of other regressors. For dummy variables this happens when you include a full set of dummies for all categories together with an intercept.

Relevant knowledge points and concepts:
- Dummy variables represent mutually exclusive categories (e.g., D1, D2, D3 for three categories).  
- The intercept term (constant) in a regression equals 1 for every observation.  
- Perfect multicollinearity: an exact linear relationship among regressors (X'X singular), which makes OLS normal equations unsolvable (no unique β̂).  
- The “dummy variable trap” is the practical name for the situation above.

Step-by-step reasoning (with a simple algebraic demonstration):
1. Suppose a categorical variable has three levels and we create three dummies D1, D2, D3, where exactly one of them equals 1 for each observation.  
2. For every observation D1 + D2 + D3 = 1. If the model contains an intercept (1) and all three dummies, we have the exact linear relation: (D1 + D2 + D3) − 1 = 0, or equivalently 1 = D1 + D2 + D3.  
3. That means one column of the design matrix is an exact linear combination of the others, so the design matrix X has linearly dependent columns and X'X is singular. OLS cannot produce unique coefficient estimates (infinite or undefined variances).  
4. To avoid the trap we omit one dummy (use a reference category) or impose a constraint (effects coding), restoring full column rank.

Why the correct answer is correct:
- The dummy variable trap is precisely an instance of perfect multicollinearity because it creates an exact, not just approximate, linear dependency.

Why the other options are incorrect:
- a. It is not merely theoretical; it occurs in practice and will break OLS estimation.  
- b. Imperfect multicollinearity refers to strong but not exact correlations; the dummy trap is exact.  
- c. This is irrelevant and false—students or datasets can easily produce the trap.

Conclusion: The correct answer is d. perfect multicollinearity. This explanation confirms and supports that choice.

The dummy variable trap is an example of:多项选择题

类似问题

You run a bunch of tests to check the assumptions of a multiple regression with two predictor variables and 100 datapoints. Which one of the following findings would indicate that one of your assumptions was violated?

The dummy variable trap is an example of:

Choose ALL CORRECT statement(s) about the imperfect multicollinearity:

Choose ALL CORRECT statement(s) about the imperfect multicollinearity:

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