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.