Answer: A linear relationship exists between the independent and the dependent variables.

## Explanation The correct answer is **D** because while a linear relationship between independent and dependent variables is indeed an assumption of OLS regression, it is **not** considered one of the **key** assumptions for parameter estimation. The three key assumptions are: 1. **Assumption B**: The expected value of the error term, conditional on the independent variable, is zero: E(εᵢ|Xᵢ) = 0 2. **Assumption A**: All (X, Y) observations are independent and identically distributed (i.i.d.) 3. **Assumption C**: It is unlikely that large outliers will be observed in the data (large outliers can create misleading regression results) ### Key Points: - **Assumption D** (linear relationship) is important but considered a non-core assumption - Other non-core assumptions include: - The model is correctly specified (includes appropriate independent variables, no omitted variables) - The independent variable is uncorrelated with the error terms - Homoscedasticity (constant variance of error terms) - No serial correlation of error terms - Error term is normally distributed ### Why D is NOT a key assumption: The linearity assumption is about the functional form of the relationship, while the three key assumptions (A, B, C) are more fundamental to ensuring the unbiasedness, consistency, and reliability of the OLS estimators. Violations of the key assumptions can lead to biased or inconsistent estimates, whereas violations of linearity might be addressed through transformations or different model specifications.

Author: Nikitesh Somanthe