Rapoport theorem: b_2pt=(y1−y2)/(x1−x2); b_std=ρσy/σx; (u1v2−u2v1)²≥0; 1−ρ²=−(ρ−1)(ρ+1)

Layer 3 — Biologyin the biogeography subtree

Sympy-exact symbolic witness of the Rapoport-rule OLS-regression + Cauchy-Schwarz-bound identities. Setup: (x_1, y_1), (x_2, y_2) two OLS observations (real); u_1, u_2, v_1, v_2 real inner-product components; ρ (correlation coefficient,…

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Explore Rapoport theorem: b_2pt=(y1−y2)/(x1−x2); b_std=ρσy/σx; (u1v2−u2v1)²≥0; 1−ρ²=−(ρ−1)(ρ+1) on the interactive knowledge graph →