Which term describes residuals with unequal variances across the levels of a predictor (the opposite of homoscedasticity)?

Which term describes residuals with unequal variances across the levels of a predictor (the opposite of homoscedasticity)?

• A. Heteroscedasticity
• B. Homoscedasticity
• C. Homogeneity of variance
• D. Heterogeneity of variance

Answer: (A)

This item is about heteroscedasticity. In regression, you assume the residuals (the differences between observed and predicted values) have the same spread at all levels of the predictor. When that spread changes across levels—getting larger or smaller as the predictor increases—that’s heteroscedasticity. It’s common to see as residuals fan out (or narrow) with higher fitted values. This matters because non-constant variance can make standard errors and hypothesis tests unreliable, even if the overall relationship is correct. Homoscedasticity is the constant-variance situation you’re aiming for. Homogeneity of variance is a related term often used in ANOVA contexts to describe equal variances across groups. Heterogeneity of variance isn’t the standard term for this regression issue, though it conveys a similar idea.

This item is about heteroscedasticity. In regression, you assume the residuals (the differences between observed and predicted values) have the same spread at all levels of the predictor. When that spread changes across levels—getting larger or smaller as the predictor increases—that’s heteroscedasticity. It’s common to see as residuals fan out (or narrow) with higher fitted values. This matters because non-constant variance can make standard errors and hypothesis tests unreliable, even if the overall relationship is correct.

Homoscedasticity is the constant-variance situation you’re aiming for. Homogeneity of variance is a related term often used in ANOVA contexts to describe equal variances across groups. Heterogeneity of variance isn’t the standard term for this regression issue, though it conveys a similar idea.