A researcher is interested in examining the relationship between the number of bears in an area (Y) and its human population (X). The scatterplot of the data is reproduced below. This scatterplot would suggest that the correlation (Pearson’s r) for this distribution would be:

Question

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The question describes examining the relationship between the number of bears (Y) and human population (X) using a scatterplot. We must infer the sign and strength of Pearson’s r from the depicted pattern.

Option A: 'A. Positive and high (e.g. +.87 ).' This would imply that as human population increases, bear numbers rise in a strong, direct relationship. However, the plotted points show that higher human populations correspond to fewer bears, not more, indicating this option misstates both the direction and the nature of the relationship.

Option B: 'B. Positive and low (e.g. +.015)'. A positive, near-zero correlation would mean almost no linear relationship but a slight upward trend. The scatter clearly demonstrates a pronounced downward pattern rather than a weak or absent association, so this is inconsistent with the graph.

Option C: 'C. Negative and high (e.g. -.87)'. Here, a strong negative linear relationship is described, meaning as X (humans) increases, Y (bears) decreases substantially. The scatterplot shows points arranged along a steep downward trend, supporting a large magnitude of negative correlation, which aligns with this option.

Option D: 'D. Negative and low (e.g. -.015)'. A negative but weak correlation would imply a slight downward trend with substantial scatter. In the plot, the points tightly hug a downward path rather than being scattered, indicating a stronger relationship than a tiny negative value. Therefore, this option underestimates the strength of the association.

To summarize the reasoning for each choice in context:
- A is incorrect because the relationship is not positive; the bear counts drop as human population grows.
- B is incorrect because the association is not positive and is not weak; the pattern is clearly downward and relatively strong.
- C is correct in characterizing both the negative direction and the high magnitude observed in the scatter.
- D is incorrect because the correlation appears strong rather than weak, given the clear downward alignment of the points.

A researcher is interested in examining the relationship between the number of bears in an area (Y) and its human population (X). The scatterplot of the data is reproduced below. This scatterplot would suggest that the correlation (Pearson’s r) for this distribution would be:单项选择题

类似问题

Which of the following values best represents the Pearson correlation for the data in the following scatterplot?