In regression analysis, which assumption states that the residuals at each level of the predictor have similar variances?

• A. Heteroscedasticity
• B. Homoscedasticity
• C. Homogeneity of regression slopes
• D. Homogeneity of covariance matrices

Answer: (B)

Constant spread of residuals across the range of the predictor is called homoscedasticity. In regression, residuals are the differences between observed values and those predicted by the model. If the variability of these residuals stays roughly the same no matter what level the predictor takes, the standard errors and hypothesis tests built on the model are valid. When the residual spread changes with the predictor—residuals fan out or funnel in—that’s heteroscedasticity and can distort inference. The other terms refer to different ideas: unequal residual spread across levels is the problem of heteroscedasticity, equal regression slopes across groups relates to whether the predictor has the same effect in different groups, and equal covariances across groups is a multivariate assumption not about single-residual variance.