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Answer: The variance of the regression residuals is the same for all observations
## Explanation For valid statistical inference in multiple linear regression (hypothesis testing, confidence intervals), the key assumptions are: - **Homoscedasticity**: The variance of regression residuals should be constant across all observations (option C) - **Normality of residuals**: For small samples, residuals should be approximately normally distributed - **Independence of errors**: Residuals should not be correlated - **Linearity**: Relationship between variables should be linear **Why other options are incorrect:** - **Option A**: Independent variables do NOT need to be normally distributed for valid inference - **Option B**: Positive correlation of residuals violates the independence assumption and makes inference invalid Homoscedasticity is crucial because heteroscedasticity (non-constant variance) leads to inefficient estimates and invalid standard errors.
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In the context of a multiple linear regression model, which of the following assumptions is required to make valid inferences about the model?
A
The independent variables are normally distributed
B
The regression residuals are positively correlated across observations
C
The variance of the regression residuals is the same for all observations
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