General Mathematics · bivariate data · manipulative

r is not the slope

The least-squares gradient is b = r × (sᵧ / sₓ). Hold r fixed and change how spread y is compared with x — the line tilts, r does not.

data ŷ = a + bx
b = r (sᵧ / sₓ)

Moments

0.80
1.60
1.20

Working