Which term describes a diagnostic tool used to analyze residuals and assess model adequacy by visual inspection?

Which term describes a diagnostic tool used to analyze residuals and assess model adequacy by visual inspection?

• A. Residual Plots
• B. Cook's Distance
• C. Ridge
• D. LASSO

Answer: (A)

Analyzing residuals with visual plots is a key diagnostic approach in regression. By plotting residuals (the differences between observed and predicted values) against fitted values or another predictor, you can see whether the errors appear random and evenly spread. If the residuals scatter around zero with no clear pattern and roughly constant variance, the model assumptions (like linearity and homoscedasticity) are likely reasonable, indicating good model adequacy. If you notice patterns—such as a curved shape, funneling spread, or clustering—that signals potential misspecification, suggesting the model may need a transformation or additional terms to capture the relationship. This visual tool focuses on residual behavior directly. Other options serve different purposes: Cook's distance flags observations that unduly influence the fitted model, while ridge and LASSO are regularization methods that shrink coefficients to improve generalization rather than diagnose residuals.

Analyzing residuals with visual plots is a key diagnostic approach in regression. By plotting residuals (the differences between observed and predicted values) against fitted values or another predictor, you can see whether the errors appear random and evenly spread. If the residuals scatter around zero with no clear pattern and roughly constant variance, the model assumptions (like linearity and homoscedasticity) are likely reasonable, indicating good model adequacy. If you notice patterns—such as a curved shape, funneling spread, or clustering—that signals potential misspecification, suggesting the model may need a transformation or additional terms to capture the relationship.

This visual tool focuses on residual behavior directly. Other options serve different purposes: Cook's distance flags observations that unduly influence the fitted model, while ridge and LASSO are regularization methods that shrink coefficients to improve generalization rather than diagnose residuals.