A Pearson correlation of 0.25 indicates that a graph of the data would show:

Question

BlackTom AI · Accepted Answer

To interpret a Pearson correlation of 0.25, consider what the correlation coefficient tells us about the relationship between two variables. A value near 0 indicates a weak or no linear relationship, whereas values closer to 1 or -1 indicate stronger linear relationships in positive or negative directions, respectively. With r = 0.25, we expect only a small positive linear association and considerable scatter around any line that shows the trend.

Option A: 'Points clustered close to a line that slopes up to the right.' Clustering near a line would correspond to a stronger positive linear relationship (a higher r value). The claim of being clustered tightly around a rising line is inconsistent with a relatively small r of 0.25, which implies more dispersion.

Option B: 'Points clustered close to a line that slopes down to the right.' A line sloping down to the right indicates a negative relationship. Since the given correlation is positive (0.25), this description would mischaracterize both the direction and the nature of the relationship.

Option C: 'Points widely scattered around a line that slopes up to the right.' This aligns with a weak positive association: there is a general upward tendency, but the individual data points are spread out, not tightly clustered, reflecting the modest magnitude of r = 0.25.

Option D: 'Points widely scattered around a line that slopes down to the right.' This describes a weak negative relationship, which contradicts the positive sign of r = 0.25, so it misstates both the slope direction and the relation strength.

Across these options, the key ideas are direction (positive versus negative) and strength (tight clustering versus wide scatter). A small positive correlation like 0.25 would not produce tight clustering around a line; rather, you’d see a line with a slight upward slope but substantial scatter around it.

A Pearson correlation of 0.25 indicates that a graph of the data would show:单项选择题

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