Solution (source code)

= Solution

Use a \b[bivariate <correlation>] to describe the direction and strength of association between two measured variables, such as study time and test score. The <Pearson correlation coefficient> describes linear association between two quantitative variables: its sign gives direction, and its magnitude reflects linear association on a standardized scale. A <confidence interval> describes estimation uncertainty; a corresponding <hypothesis test> can assess a specified null association under its sampling assumptions.

Inspect a <scatter plot> for curvature, clusters, influential observations and <restriction of range>. A coefficient near zero does not exclude a strong nonlinear relationship. For ordered or markedly nonnormal measurements, a <Spearman rank correlation> can describe monotone association, using ranks; it does not require a linear relation in the original units. Ordinary inferential procedures require independent observational units and appropriate assumptions for their chosen method. \b[<Correlation> alone does not identify a causal direction or exclude <confounding>.]