In the pulse experiment data, which statement is correct for the correlation between weight and pulse1?

Question

BlackTom AI · Accepted Answer

Pearson's r = -0.173 indicates a slight inverse linear association between weight and pulse1.

1) Relevant concepts
- Pearson correlation coefficient (r) measures the strength and direction of a linear relationship between two continuous variables; r ranges from -1 to +1. 
- The sign (+/−) gives direction (positive: both increase together; negative: one increases as the other decreases). 
- The magnitude indicates strength. Common interpretive guidelines: |r| < 0.2 (very weak), 0.2–0.39 (weak), 0.4–0.59 (moderate), 0.6–0.79 (strong), ≥0.8 (very strong). 
- Coefficient of determination r^2 gives the proportion of variance in one variable explained by the other.

2) Step-by-step reasoning
- The reported correlation is r = -0.173. The negative sign means the relationship is inverse: as weight increases, pulse1 tends to decrease slightly.  
- Assess magnitude: |−0.173| = 0.173, which falls below 0.2 and certainly below the 0.3 threshold for a “medium” effect; thus it should be described as a very weak or weak negative relationship by standard conventions.

3) Calculations (intermediate steps)
- Compute r^2 to quantify explained variance: r^2 = (−0.173)^2 = 0.029929 ≈ 0.03.
- In percentage terms, r^2 × 100% ≈ 2.99%. Thus only about 3% of the variation in pulse1 is linearly explained by weight.

4) Why the correct answer is correct
- The negative sign gives the direction (negative), and the numerical magnitude (0.173) is small. Combining those facts yields the description “a weak negative relationship.” The r^2 calculation reinforces that the association explains very little variance (≈3%), consistent with being weak.

5) Why other possible choices would be incorrect
- “Strong negative” would be incorrect because |r| = 0.173 is far below thresholds for strong relationships (generally ≥0.6). 
- “Weak positive” would be incorrect because the sign is negative, not positive. 
- “No relationship” would be misleading: r is not zero, so a small negative linear tendency exists, even if it is weak and possibly not practically significant.

6) Conclusion
The data show a correlation coefficient of −0.173, indicating a weak negative relationship (about 3% variance explained). This confirms the provided answer: "The correlation coefficient is -0.173, a weak negative relationship."

In the pulse experiment data, which statement is correct for the correlation between weight and pulse1?单项选择题

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