Question 1164939: The normality assumption implies that:a. the population error u is dependent on the explanatory variables and is normally distributed with mean equal to one and variance 2b. the population error u is independent of the explanatory variables and is normally distributed with mean equal to one and variance c. the population error u is dependent on the explanatory variables and is normally distributed with mean zero and variance d. the population error u is independent of the explanatory variables and is normally distributed with mean zero and variance 2.
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Answer by CPhill(2189)   (Show Source):
You can put this solution on YOUR website! Based on the standard Gauss-Markov assumptions for classical linear regression models, the correct answer is **d**.
The **normality assumption** specifically states that the population error term () is **independent** of the explanatory variables () and is **normally distributed** with a mean of **zero** and a constant variance ().
### Breakdown of the Assumption:
* **Independence:** The error term must not be related to the explanatory variables. If they were dependent, the estimates for your coefficients would be biased.
* **Mean Zero ():** We assume that, on average, the errors cancel each other out. Any non-zero mean is typically absorbed into the intercept () of the model.
* **Constant Variance ():** Also known as homoscedasticity, this implies the "spread" of the errors remains constant across all levels of the explanatory variables.
* **Normal Distribution:** This allows us to conduct hypothesis tests (like t-tests and F-tests) because it ensures that the sampling distributions of our estimators are also normal.
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### Why the other options are incorrect:
* **a & c:** The error term cannot be dependent on the explanatory variables; this violates the assumption of exogeneity.
* **a & b:** The mean of the error term must be **zero**, not one. If the mean were one, the model would systematically over-predict or under-predict the dependent variable.
Would you like me to explain how violating this assumption affects the reliability of your p-values?
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