Which statement explains why correlation could be 0 even if a strong relationship between two variables existed?

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BlackTom AI · Accepted Answer

The question asks why correlation could be 0 even if a strong relationship between two variables exists.
First, recognize what correlation measures: Pearson correlation assesses the strength and direction of a linear relationship between two variables. It does not detect nonlinear patterns.
Because of this, a strong nonlinear association (for example, a perfect curve) can produce a correlation near zero if the data do not align linearly.
Second, consider why the available options matter. In this case, there is only one provided answer: 'Correlation does not describe curved (nonlinear) relationships between variables.' This statement targets the core limitation of correlation as a linear measure, which explains why the correlation could be zero despite a strong relationship.
Third, if a relationship is nonlinear but monotonic (consistently increasing or decreasing, though not at a constant rate), sometimes nonparametric or rank-based measures (like Spearman's rho) may capture it better than Pearson's r, whereas Pearson's r would still potentially be near zero if the curve is strongly curved.
Fourth, think about alternative explanations that can drive correlation to zero in practice: a limited or restricted range of data, a small sample size, or the presence of outliers can all attenuate or obscure the linear association even when a relationship exists in the broader population.
Fifth, since the prompt’s answer options are not provided here, there is no basis to evaluate other choices. The key idea remains: Pearson correlation specifically assesses linear association, so nonlinearity can yield a zero correlation even if a meaningful relationship is present in the data.

STAT 1450.02 SP2025 (28132) Checkpoint 4.5 & 4.6

Which statement explains why correlation could be 0 even if a strong relationship between two variables existed?

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