A COLLECTION OF CONNECTIONSSame math.
Different stories.
Seven datasets to sharpen your intuition. Every example is simulated for teaching, not evidence about the real world.
01 / STRONG POSITIVEStudy hours × exam score
More study time accompanies higher scores in this simulated sample. Prior knowledge, teaching and many other factors still matter.
r = 0.870
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02 / WEAK POSITIVEHeight × weight
A weak positive association with substantial individual variation. These illustrative measurements are synthetic.
r = 0.300
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03 / STRONG NEGATIVEExercise × resting heart rate
Higher exercise values accompany lower resting heart rates in this simulated dataset. An observational relationship is not a causal conclusion.
r = -0.860
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04 / TEMPERATURE & SALESTemperature × ice cream sales
A simulated seasonal relationship. Temperature can also explain a correlation between ice cream sales and swimming activity.
r = 0.760
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05 / NO CORRELATIONUnrelated variables
These synthetic coordinates are constructed to have zero sample linear correlation. Random samples will not usually have exactly zero r.
r = -0.000
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06 / NONLINEAR RELATIONSHIPA relationship hiding in plain sight
The U-shape is perfectly predictable, yet Pearson r is zero. Always look at the scatter plot before interpreting a number.
r = 0.000
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07 / OUTLIER EXAMPLEOne point. A different story.
An extreme point can substantially change Pearson r. A flag is an invitation to investigate, never permission to discard an observation.
r = -0.433
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