Which term describes the condition opposite to homoscedasticity, where residual variances differ across the range of predictor values?

Which term describes the condition opposite to homoscedasticity, where residual variances differ across the range of predictor values?

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

Answer: (D)

The condition is heteroscedasticity. It describes a situation where the spread (variance) of the residuals changes across the range of the predictor values, rather than staying roughly constant. This is the opposite of homoscedasticity, where residual variances are constant regardless of the predictor level. It’s different from normality, which concerns the shape of the residuals’ distribution, and from homogeneity of variance, which is another term for constant variance (i.e., homoscedasticity). When heteroscedasticity is present, standard errors from ordinary least squares can be biased, affecting hypothesis tests; you might address it with robust standard errors, a transformation of the response, or weighted least squares.

The condition is heteroscedasticity. It describes a situation where the spread (variance) of the residuals changes across the range of the predictor values, rather than staying roughly constant. This is the opposite of homoscedasticity, where residual variances are constant regardless of the predictor level. It’s different from normality, which concerns the shape of the residuals’ distribution, and from homogeneity of variance, which is another term for constant variance (i.e., homoscedasticity). When heteroscedasticity is present, standard errors from ordinary least squares can be biased, affecting hypothesis tests; you might address it with robust standard errors, a transformation of the response, or weighted least squares.