Cook's distance is a measure of what in regression analysis?

• A. Leverage
• B. Residual variance
• C. Cook's distance
• D. Standardized residuals

Answer: (C)

Cook's distance measures how influential a single observation is on the fitted regression results. It asks: if we remove that point, how much would the estimated coefficients change? It combines two ideas—leverage (how far the point’s x-values are from the center of the data) and the size of its residual (how far the observed y is from the model’s prediction). A point with high leverage and a large residual can substantially alter the regression equation, so its Cook's distance is large.

This is why it’s the best choice here: it specifically quantifies influence on the model, not just the potential to influence (leverage), not the overall residual spread (residual variance), and not the standardized size of a residual (standardized residuals). Large values flag observations that deserve closer inspection for data entry errors, model misspecification, or the need for model revisions. As a rough guide, Cook’s distance values well above 1 or above 4/n (depending on context) suggest influential observations.