Problem

Compare \(r=0.91\) with a far-right point and \(r=0.46\) without it. Describe the change in \(|r|\), the point's effect on the positive correlation, the result's sensitivity, and what cannot be concluded about error or causation.

Paired scatterplots compare the same six-point cluster with and without one far-right high point; one plot contains the red influential point and the other omits it; correlation values are not annotated.

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What this problem is really about

Influence is diagnosed by asking how much the statistic changes when one point is removed, while also comparing the two scatter patterns. A far-out point aligned with the trend can strengthen correlation rather than weaken it; a large change signals sensitivity, not automatic evidence of error, deletion, or causation.

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Removing the point lowers r from 0.91 to 0.46, so the point must be a data-entry error that should automatically be deleted.

Removing the point lowers |r| from 0.91 to 0.46, so the point proves that the variables have a causal relationship.

Removing the point lowers |r| from 0.91 to 0.46, so the point strongly increases the measured positive correlation and the result should be reported as sensitive to that point.

Removing the point lowers |r| from 0.91 to 0.46, so the remaining data still show a strong positive correlation.

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Compare \(r=0.91\) with a far-right point and \(r=0.46\) without it. Describe the change in \(|r|\), the point's effect on the positive correlation, the result's sensitivity, and what cannot be concluded about error or causation.

What this problem is really about

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