Which statement correctly lists common regression assumptions related to residuals?

Which statement correctly lists common regression assumptions related to residuals?

• A. Linearity, homoscedasticity, independence
• B. Linearity, heteroscedasticity, autocorrelation
• C. Nonlinearity, homogeneous variance, independence
• D. Linearity, heteroscedasticity, independence

Answer: (A)

Residuals in regression are expected to behave in a way that reflects a properly specified linear relationship. The key ideas are that the relationship between predictor and outcome is linear, the spread of residuals is roughly the same across all fitted values (constant variance, or homoscedasticity), and the residuals are independent from one observation to the next (no autocorrelation). When you check a residuals plot, a nice fit shows no curved pattern, the residuals spread evenly as fitted values increase, and no obvious sequence or clustering of residuals appears. If any of these expectations fail—curvature suggesting nonlinearity, increasing or decreasing spread indicating heteroscedasticity, or a pattern over time or order indicating dependence—the model assumptions are violated and inference can be unreliable. The option that lists linearity, constant variance, and independence captures these standard residual-related assumptions. The other choices mix in nonlinearity or heteroscedasticity as if they’re assumptions, which signals model misspecification rather than acceptable conditions.

Residuals in regression are expected to behave in a way that reflects a properly specified linear relationship. The key ideas are that the relationship between predictor and outcome is linear, the spread of residuals is roughly the same across all fitted values (constant variance, or homoscedasticity), and the residuals are independent from one observation to the next (no autocorrelation). When you check a residuals plot, a nice fit shows no curved pattern, the residuals spread evenly as fitted values increase, and no obvious sequence or clustering of residuals appears. If any of these expectations fail—curvature suggesting nonlinearity, increasing or decreasing spread indicating heteroscedasticity, or a pattern over time or order indicating dependence—the model assumptions are violated and inference can be unreliable. The option that lists linearity, constant variance, and independence captures these standard residual-related assumptions. The other choices mix in nonlinearity or heteroscedasticity as if they’re assumptions, which signals model misspecification rather than acceptable conditions.