Correlation Heatmap & Pair-Plot Explorer

Dataset

Sample size N 150

Target corr(A, B) 0.70

Measurement noise 0.10

Live Readouts

Pearson r(A,B)

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t-statistic

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Significance (df=N−2)

n/a

Mean |r| (matrix)

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How it works

Five variables (A–E) are generated so their true population correlations are known: A and B follow the standard construction for a target correlation ρ,

z1, z2 ~ N(0,1) independent
A = z1
B = ρ·z1 + √(1−ρ²)·z2   ⇒  Corr(A,B) = ρ

C and D are built the same way with a fixed ρ = −0.6 (a clean negative example), and E is pure independent noise. Every value then gets extra i.i.d. Gaussian noise scaled by the "measurement noise" slider, which attenuates the observed correlation below the true ρ — the same regression-dilution effect that shows up in real sensor and survey data.

The heatmap shows the empirical Pearson correlation matrix, r_ij = cov(X_i,X_j) / (σ_iσ_j), as coloured bars (blue = negative, red = positive, white = ~0); the side panel plots the raw A–B scatter the r(A,B) cell is computed from. Significance of r(A,B) uses the standard test statistic

t = r·√((N−2) / (1−r²)),  df = N−2
|t| > ~1.96  →  p < 0.05 (two-tailed, large-N approx.)

Sample size N — more samples shrink sampling noise and make the empirical r track the true ρ more tightly.
Target corr(A,B) — sets the population correlation ρ used to generate A and B.
Measurement noise — post-hoc noise added to every variable, which always weakens the observed correlation, never strengthens it.
Resample — draws a brand-new random dataset from the same settings, showing how much the matrix jitters from sample to sample.

Positive correlation ~0 correlation Negative correlation

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