Which of the following exhibits the strongest linear relationship between the X and Y variable?

A B C D

Question

Which of the following exhibits the strongest linear relationship between the X and Y variable?

A	B	C	D

BlackTom AI · Accepted Answer

A strong linear relationship is visible when the points lie close to a single straight line (small vertical scatter around the line), producing a high absolute Pearson correlation (|r| close to 1). Key concepts: direction (positive or negative slope), strength (tightness of points around a line), and linearity (consistent change in Y for change in X).

Step-by-step reasoning:
1. Inspect plot A: points alternate up and down in a regular wave-like pattern. Although there is structure, it is clearly non‑linear (periodic). For a linear fit the residuals would be large and r would be near 0. So A is not a strong linear relationship.
2. Inspect plot B: points form several vertical clusters with substantial vertical spread inside clusters. There is no single consistent trend across x; the variability within x values is large, yielding a low linear correlation. So B is weakly linear (if at all).
3. Inspect plot C: points show a positive trend (as x increases, y tends to increase). However the scatter around that upward trend is moderate — points are moderately dispersed rather than tightly packed on a line. This implies a moderate positive correlation (say r maybe 0.5–0.7), not the strongest.
4. Inspect plot D: points lie closely along a straight, downward‑sloping line with very little scatter around that line. This indicates a very strong negative linear relationship; the absolute correlation |r| would be very close to 1 (e.g., r ≈ −0.9 or lower). Minimal vertical spread means regression residuals are small and linear model explains most variance.

Why D is correct: D exhibits the smallest deviations from a straight line and a consistent negative slope, which maximizes the magnitude of the linear correlation. Why the others are incorrect: A is non‑linear (periodic), B is clustered with large within‑cluster spread (no clear single linear trend), and C is only moderately linear (more scatter than D).

Therefore the strongest linear relationship is D, which matches the provided correct answer: D.

Which of the following exhibits the strongest linear relationship between the X and Y variable? A B C D 单项选择题

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