What is homoscedasticity?

What is homoscedasticity?

• A. Normal distribution of residuals
• B. Constant variance of residuals across levels of the predictor
• C. Residuals are independent of the predictor
• D. Constant mean of residuals

Answer: (B)

Homoscedasticity means the residuals (the differences between observed and predicted values) have the same spread across all levels of the predictor. In other words, the variance of the residuals is constant no matter what value the predictor (or fitted value) takes. If you plot residuals against the predictor and the spread stays roughly the same, that supports homoscedasticity. If the spread gets wider or narrower as the predictor increases, that’s heteroscedasticity, which can lead to biased standard errors and unreliable inference. This is not about the residuals being normally distributed, which is a separate assumption, nor about residuals being independent of the predictor, which relates to independence or correlation patterns, nor about the residuals having a constant mean (the mean is typically around zero with an intercept).

Homoscedasticity means the residuals (the differences between observed and predicted values) have the same spread across all levels of the predictor. In other words, the variance of the residuals is constant no matter what value the predictor (or fitted value) takes. If you plot residuals against the predictor and the spread stays roughly the same, that supports homoscedasticity. If the spread gets wider or narrower as the predictor increases, that’s heteroscedasticity, which can lead to biased standard errors and unreliable inference.

This is not about the residuals being normally distributed, which is a separate assumption, nor about residuals being independent of the predictor, which relates to independence or correlation patterns, nor about the residuals having a constant mean (the mean is typically around zero with an intercept).