Correlation — Feel r Through Scatter Plots
Draw scatter plots freely and feel how the correlation coefficient r shifts between −1 and +1. Four-quadrant coloring reveals the formula's meaning. Anscombe's quartet shows why numbers alone aren't enough.
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Correlation — Measuring the Link Between Two Variables
The chi-squared test quantified associations between categories. But how do we measure the relationship between continuous numbers — height vs. weight, study time vs. test scores? → The correlation coefficient r compresses "how much they move together" into a single number from −1 to +1.
The correlation coefficient r measures whether two variables move together. +1 means a perfect positive linear relationship, −1 a perfect negative one, 0 means no linear relationship. Click the canvas to add points and watch r update in real time. The yellow dashed lines mark the means, splitting the space into four quadrants — more points in green quadrants means positive correlation, more in red means negative. This coloring is the "tug-of-war of signs" in the formula Σ(x−x̄)(y−ȳ).
Experiment Guide — Feel the Correlation
- Step 1: Set r = 0.80, click Generate → an upward-sloping band. Points cluster in the green quadrants.
- Step 2: Change to r = −0.60, Generate → downward slope. More points in the red quadrants.
- Step 3: Set r = 0.00, Generate → points spread evenly across all four quadrants. A "cloud," not a band.
- Step 4: CLEAR, then manually place a U-shape → r ≈ 0 yet there's an obvious pattern! r only captures linear relationships.
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Correlation r—
R²—
Covariance—
Experiment Guide — Peek Behind the Numbers
- Step 1: Watch the animation. Points appear one by one, patterns look totally different…
- Step 2: Check each plot's r ≈ 0.816. They're all nearly identical!
- Step 3: Regression lines appear → lines are nearly identical too. Yet II is curved, III has an outlier, IV is dominated by one point.
- Step 4: Click "Replay" to watch again. Numbers alone don't tell the whole story.