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Relationships 1
Paired plots: Plot paired explanatory and response values.
Direction and strength: Strength is closeness, not gradient.
Causation and confounding: Correlation can have alternative explanations.
Double mean point: A fitted line passes through the double mean.
Relationships 2
Interpolation: Predict inside observed range with uncertainty.
Extrapolation: Beyond-range predictions can fail.
Gradient and intercept: Slope has response units per explanatory unit.
Given rank coefficient: Spearman measures agreement of rankings.
H: coefficients 1
Higher: Regression equation: Substitute in y = a + bx; respect direction.
Higher: Rank and differences: Pair consistent ranks; square their differences.
Higher: Spearman calculation: Rank coefficient from summed squared differences.
Higher: PMCC: PMCC measures linear association, not all patterns.
H: coefficients 2
Higher: Compare coefficients: Monotonic rank trend differs from linear fit.
Connections
Relationships 1 → Relationships 2: A fitted trend and its double mean support qualified interpolation and extrapolation.
H: coefficients 1 → H: coefficients 2: Spearman uses rankings while PMCC specifically describes linear numerical association.