Which assumption states that the residuals should be normally distributed?

• A. Normality of residuals
• B. Linearity
• C. Independence
• D. Homoscedasticity

Answer: (A)

Normality of residuals is about the distribution of the errors the model can’t explain. In regression, residuals are the differences between what you observe and what the model predicts. The assumption is that these residuals come from a normal distribution with mean zero and constant variance. This normality underpins the reliability of significance tests for the coefficients (like t-tests) and the construction of confidence intervals, especially with smaller samples. If residuals look roughly normal, the usual inferences are more trustworthy; if they’re clearly non-normal (skewed, heavy-tailed, or with outliers), it can signal model misspecification or the need for a data transformation, and inference may be less reliable. The other listed assumptions—linearity (the relationship should be linear), independence (residuals should be uncorrelated), and homoscedasticity (constant variance across fitted values)—relate to the shape of the relationship, error independence, and consistent spread, but they do not specify the distribution of residuals.