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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To begin, let's restate what the question is asking: interpret the relationship between the number of bears (Y) and human population (X) as depicted by the scatterplot, and infer the sign and strength of Pearson’s r.
Option A: Positive and high (e.g., +.87). This would imply that as human population increases, bear numbers also increase in a strong, direct way. The scatterplot shown has bears decreasing as humans increase, so this option contradicts the visual pattern.
Option B: Positive and low (e.g., +.015). A tiny positive correlation would mean a very weak tendency for higher human population to be associated with slightly more bears. But the plotted points clearly move in the opposite direction overall, so a positive association is not only weak but also opposite in direction to what the data show.
Option C: Negative and high (e.g., -0.87). This choice describes a strong inverse relationship: as human population rises, bear numbers fall substantially. Looking at the scatterplot, there is a clear downward trend: higher X values (more humans) correspond to lower Y values (fewer bears), which aligns with a strong negative correlation.
Option D: Negative and low (e.g., -0.015). This would indicate a very weak inverse relationship, almost no association. However, the plotted points do not scatter randomly with no pattern; they exhibit a pronounced downward pattern, indicating a substantial negative association rather than a nearly flat one.
In summary, the core misconception in the incorrect options would be misreading the direction (positive instead of negative) or misjudging the strength (weak vs. strong) of the relationship. The visual pattern is best described by a strong negative association, where increases in humans correspond to large decreases in bear counts. Therefore, the negative direction with high magnitude correctly captures the observed relationship in the scatterplot.

PSYC20009_2025_SM2 Lecture 3 Quiz

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:

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类似问题

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

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

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

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:

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

This is the formula for [ Select ] Pearson’s r correlation z-test for an individual score between-subjects t-test pooled variance .

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