Which methods are commonly used to assess whether residuals in a regression are approximately normally distributed?

• A. Q-Q plot and histogram.
• B. Only to check the mean of the residuals.
• C. Q-Q plot, Shapiro-Wilk test, Kolmogorov-Smirnov test, and histogram examination.
• D. Visually inspecting the dependent variable.

Answer: (C)

Evaluating whether regression residuals come from a normal distribution uses both visual checks and formal tests to get a clear picture of the distribution’s shape. A Q-Q plot helps by plotting the residuals against the expected values from a normal distribution; if the points roughly lie on a straight line, that suggests the residuals are approximately normal. A histogram gives a quick snapshot of the distribution’s shape—look for a symmetric, bell-shaped curve as a sign of normality, while skewness or multiple peaks signal departures.

Formal tests add objectivity. The Shapiro-Wilk test provides a p-value indicating whether the residuals plausibly come from a normal distribution, and it tends to be quite powerful for typical sample sizes. The Kolmogorov-Smirnov test offers another way to compare the residuals’ empirical distribution to a normal reference distribution, though it can be less sensitive than Shapiro-Wilk when parameters are estimated from the data. Using both the visual tools and these tests together gives a more reliable assessment of normality than any single method.

This approach matters because normality of residuals underpins the validity of many regression inferences. Merely checking the mean of the residuals or inspecting the dependent variable does not inform you about the residuals’ distribution, so those options miss the key issue.