Answer: regression residuals are normally distributed.

## Explanation In simple linear regression, the normality assumption specifically applies to the **regression residuals** (also called error terms), not to the dependent or independent variables themselves. ### Key Points: 1. **Normality of Residuals**: The classical linear regression model assumes that the error terms (ε) are normally distributed with mean zero and constant variance σ². 2. **Why Residuals, Not Variables**: - The dependent variable (Y) can have any distribution; it's the conditional distribution of Y given X that matters - The independent variable (X) can be fixed or random; no normality assumption is required for X - The residuals represent the unexplained variation after accounting for the linear relationship 3. **Importance**: This assumption is crucial for: - Valid hypothesis testing (t-tests, F-tests) - Constructing confidence intervals - Making predictions with proper uncertainty quantification 4. **Central Limit Theorem**: Even if residuals aren't perfectly normal, with large sample sizes, inference is often robust due to the Central Limit Theorem. ### Mathematical Representation: The regression model: Y = β₀ + β₁X + ε Where ε ~ N(0, σ²) This means the residuals should be approximately normally distributed around zero.

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