Which description best matches a well-specified regression model in terms of residuals?

• A. Residuals show a clear trend when plotted against fitted values
• B. Residuals increase with fitted values
• C. Residuals are randomly scattered with constant variance around zero
• D. Residuals have a diagonal pattern

Answer: (C)

For a regression model to be well specified, the residuals—the differences between observed values and what the model predicts—should behave like random noise with no systematic pattern. When you plot them against the fitted values, they should form a roughly horizontal cloud centered near zero, with similar spread across the entire range. That indicates the model has captured the underlying relationship and the assumptions of linearity and constant variance hold. If the residuals show a trend, funnel, or changing spread as fitted values grow, it suggests misspecification or heteroscedasticity. A diagonal pattern or any structured pattern implies deliberate dependencies or other issues in the data. So the description of residuals being randomly scattered with constant variance around zero best matches a well-specified regression model.