Current correlation
r = 0.000
n=200
cov(x,y)=0.000
σx=0.000
σy=0.000
1.00
0.25
200
Generator (fixed axes): we sample a latent
t in [-1, 1], then
x = t + noise·zx and y = slope·t + noise·zy,
where zx, zy are standard normal. So the same noise level
“blurs” both axes.
r = cov(x, y) / (σx · σy) cov(x, y) = (1/(n-1)) · Σ (xi - x̄)(yi - ȳ) σx = sqrt( (1/(n-1)) · Σ (xi - x̄)² ) σy = sqrt( (1/(n-1)) · Σ (yi - ȳ)² )
Interpretation: |r| → 1 means tight linear alignment; |r| → 0 means little linear association.
Scatter plot
Fixed domain: x ∈ [-3, 3], y ∈ [-3, 3]. Zero lines and best-fit line shown.