The scatterplot below represents percent of lean body mass and resting pulse rate. Is there a linear relationship visible? If so, what would you expect the correlation coefficient to be?Single choice
A
Yes, 𝑟 ≈ − 0.18
B
Yes, 𝑟 ≈ 0.27
C
Yes, 𝑟 ≈ − 0.82
D
Yes, 𝑟 ≈ 0.84

Question

The scatterplot below represents percent of lean body mass and resting pulse rate. Is there a linear relationship visible? If so, what would you expect the correlation coefficient to be?

BlackTom AI · Accepted Answer

The points show a clear upward trend, indicating a positive linear relationship; the best choice is Yes, r ≈ 0.84.

1) Relevant concepts and knowledge points
- Correlation coefficient r measures the direction and strength of a linear relationship: sign (+/−) for direction, magnitude (0 to 1) for strength. Values near 0 indicate little linear association; values near ±1 indicate strong linear association.
- Visual assessment: direction (upward or downward), form (linear or nonlinear), and scatter tightness (how close points lie to an imagined straight line) guide an expected r.

2) Step-by-step reasoning process
- Direction: The scatterplot’s points clearly rise as Mass increases, so the correlation must be positive.
- Form: The points approximate a straight-line pattern rather than a curve, so a linear r is appropriate.
- Strength: Points lie fairly close to an imagined straight line with only moderate spread—this implies a fairly strong positive correlation, not weak or negligible.

3) Calculations / intermediate numeric check
- A quick slope estimate using two extreme-ish points: Δy/Δx = (85 − 55) / (62 − 37) = 30 / 25 = 1.2. This positive slope reinforces a positive linear relationship.
- No precise r is required from the plot, but the compactness about the line (moderate-to-small vertical scatter) suggests r well above 0.5, likely in the 0.7–0.9 range.

4) Why the correct answer is correct
- Among the options given, the only large positive value is r ≈ 0.84. Because the plotted points show a clear, fairly tight positive linear trend, a strong positive correlation like 0.84 matches the visual evidence.

5) Why the other options are incorrect
- r ≈ −0.18: wrong sign (negative) and near zero; contradicts the clear upward trend.
- r ≈ 0.27: positive but far too small for the visibly strong linear pattern.
- r ≈ −0.82: wrong sign (negative) despite the upward trend; magnitude otherwise large but sign makes it incorrect.

6) Conclusion
The scatterplot displays a strong positive linear relationship, so the best match is Yes, r ≈ 0.84, which confirms the provided answer.

The scatterplot below represents percent of lean body mass and resting pulse rate. Is there a linear relationship visible? If so, what would you expect the correlation coefficient to be?Single choice

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