Homoscedasticity means

• A. The residuals are normally distributed.
• B. The variance of residuals is constant across levels of the predictor.
• C. The residuals sum to zero.
• D. The residuals are correlated with the predictor.

Answer: (B)

Homoscedasticity means the spread of the residuals stays the same across the range of the predictor (or across fitted values). In a clean linear regression, the residuals should have constant variance no matter where you are on the x-axis. If you plot residuals against the predictor or against fitted values and see the vertical spread widening or narrowing at higher levels, that’s a sign of heteroscedasticity. This matters because the usual inferences from ordinary least squares rely on this constant variance; when it’s not present, the standard errors for the coefficients can be biased, making t-tests and confidence intervals unreliable, even though the coefficient estimates themselves may still be unbiased.

Other statements describe different aspects: residuals being normally distributed relates to distributional assumptions rather than variance across levels; the residuals summing to zero is a property of the least-squares solution, not about equal spread; and residuals being correlated with the predictor would indicate a different kind of misspecification, not homoscedasticity.