Next, Gladly looks at Cook's distance and obtains the plot below for the model m2.

What does this plot indicate?

Question

Next, Gladly looks at Cook's distance and obtains the plot below for the model m2.

What does this plot indicate?

BlackTom AI · Accepted Answer

Cook's distance measures how much removing each observation changes all fitted values; it combines both the residual (outlyingness) and leverage (distance in predictor space) into a single influence measure.

Step-by-step reasoning:
1. Read the plot: the y-axis is Cook's distance and the tallest bars are labeled (observations) 10, 82, and 120. The maximum Cook's D visible is roughly 0.12 (well below 1.0).
2. Apply common rule-of-thumb thresholds: the most widely used threshold for a clearly influential point is Cook's D > 1.0. A more sensitive threshold sometimes used is 4/n (or 4/(n − p − 1)), but that threshold depends on sample size n and is typically only used when explicitly computed. The plot’s maximum (~0.12) is far below 1.0.
3. Interpret: since none of the observations approach or exceed 1.0, none are strongly influential in the sense of unduly altering the regression fit. The few taller bars simply indicate relatively larger influence compared with the rest of the sample, but their absolute Cook’s D values remain small.

Why the correct answer is correct:
- Because no Cook’s distance exceeds the standard threshold for high influence (1.0), we conclude there are no high-influence points.

Why the other choices are incorrect:
- “There are multiple high-influence points.” Incorrect because none of the Cook’s D values approach the conventional cutoff of 1.
- “There are multiple high-leverage points.” Cook’s distance does not directly report leverage (hat values); high leverage must be assessed from hat-values, not this plot.
- “There are no high-leverage points.” Cannot be concluded from Cook’s D alone.
- “There are multiple outliers but none of them are worrisome.” Outliers are diagnosed from residuals; Cook’s D suggests no observation has appreciable influence, so labeling them as outliers isn’t supported here.

Conclusion: The plot indicates there are no high-influence points, which matches the provided answer.

Next, Gladly looks at Cook's distance and obtains the plot below for the model m2. What does this plot indicate?Single choice

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