Strength vs Steepness: Correlation & Slope
Change correlation strength without changing line steepness, and vice versa. (Direction is shared.)
📊 Correlation
01
WeakMediumStrong
Bounded: |r| is always between 0 and 1. Increasing it makes points hug the line more tightly.
📐 Slope
FlatMediumSteep
Unbounded: slope can be any value. Increasing steepness rotates the best-fit line without changing correlation strength (if |r| is held fixed).
Exploration
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Make |r| strong (above ~0.6). Notice it never exceeds 1.
Increase Strength (|r|) slider.
Flip the r and slope cards to check your values →
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Show the axes to see the coordinate system.🔒Make slope steep (above ~1.5). Notice slope isn't bounded.
🔒Change correlation without changing slope (aim |slope| ≈ 1.0 but |r| weak).
🔒Change slope without changing correlation (aim |r| ≈ 0.8 but slope very steep).
💡 Key Insights
Strength vs Steepness: |r| controls how tightly points hug a line (bounded 0–1). Slope controls the line's steepness (unbounded).
Direction shared: when both are computed globally, the sign of r matches the sign of the best-fit slope.
Independent magnitudes: you can change |r| without changing slope magnitude, and change slope magnitude without changing |r|—that's what the sliders demonstrate.