Normality of residuals is important for

• A. The predictor is biased.
• B. Estimating regression coefficients.
• C. Predicting individual outcomes.
• D. Inference about population parameters.

Answer: (D)

Normality of residuals matters for making inferences about population parameters in regression. When the residuals are (approximately) normally distributed, the sampling distribution of the estimated coefficients follows a t-distribution, allowing us to compute valid p-values and confidence intervals for the true population values. This makes hypothesis tests about the parameters and interval estimates reliable in small samples. If residuals deviate from normality, those exact tests and intervals can be less trustworthy, though large samples often mitigate this with the Central Limit Theorem. The normality assumption isn’t what guarantees the predictor is unbiased, nor is it strictly needed for predicting the average outcome or for point estimates themselves. Its main role is enabling accurate inference about population parameters.