📊 Topic Summary
This printable activity focuses on practicing the Gauss-Markov assumption checks essential for Ordinary Least Squares (OLS) regression. These assumptions, when met, guarantee that OLS estimators are the Best Linear Unbiased Estimators (BLUE). Understanding and verifying these assumptions is crucial for ensuring the reliability and validity of regression results.
The Gauss-Markov theorem relies on the following assumptions about the error term: it has a mean of zero, it is uncorrelated with the independent variables, it has constant variance (homoscedasticity), and the errors are not correlated with each other (no autocorrelation). This worksheet includes activities to help you solidify your understanding of these key concepts.
🧠 Part A: Vocabulary
Match the following terms with their correct definitions:
| Term |
Definition |
| 1. Homoscedasticity |
A. The error term has a mean of zero. |
| 2. Exogeneity |
B. The variance of the error term is constant across all levels of the independent variables. |
| 3. Autocorrelation |
C. The error term is uncorrelated with the independent variables. |
| 4. Zero Conditional Mean |
D. The error terms are uncorrelated with each other. |
| 5. BLUE |
E. Best Linear Unbiased Estimator. |
✍️ Part B: Fill in the Blanks
Complete the following paragraph with the correct terms:
The Gauss-Markov theorem states that under certain assumptions, OLS estimators are __________. This means they are the most __________ estimators among all __________ estimators. One crucial assumption is __________, which implies that the variance of the error term is constant. Another key assumption is that the error term has __________ and is uncorrelated with the __________. If these assumptions are violated, the OLS estimators may be biased or inefficient.
🤔 Part C: Critical Thinking
Explain, in your own words, why checking the Gauss-Markov assumptions is essential before interpreting the results of an OLS regression.