Which regression assumption concerns a constant variance of residuals across fitted values?

• A. Linearity
• B. Independence
• C. Homoscedasticity
• D. Normality of residuals

Answer: (C)

The key idea is that the spread of the residuals should be the same no matter what value the model predicts. In linear regression, this constant spread of residuals across all fitted values is called homoscedasticity. When the residuals become more spread out as fitted values increase or decrease, that changing variance is heteroscedasticity, which can make standard errors and hypothesis tests unreliable even though the estimates of the coefficients may still be unbiased. So this question is asking about maintaining a constant variance of residuals across the range of fitted values, which is exactly homoscedasticity. Linearity refers to the straight-line relationship, independence to residuals not being correlated, and normality to the residuals’ distribution—these are different assumptions. A residuals vs fitted values plot is a common way to check for this: a roughly uniform spread indicates correctness, while a funnel or increasing/decreasing spread signals a problem.