Geometric Interpretation of Pearson's Correlation Coefficient (Draft)

GeoGebra Commands & Parameters

1. OrthogonalLine(B, b) → c
2. Intersect(b, c) → E
3. Intersect(a, b) → meanxy
4. OrthogonalLine(C, b) → e
5. OrthogonalLine(D, b) → f
6. OrthogonalLine(B, a) → g
7. OrthogonalLine(A, a) → h
8. OrthogonalLine(A, b) → i
9. OrthogonalLine(C, a) → j
10. OrthogonalLine(D, a) → k
11. Intersect(b, e) → G
12. Intersect(b, f) → H
13. Intersect(b, i) → I
14. Intersect(a, h) → J
15. Intersect(a, g) → K
16. Intersect(a, j) → L
17. Intersect(a, k) → M
18. Vector(E, B) → B_x
19. Vector(I, A) → A_x
20. Vector(G, C) → C_x
21. Vector(H, D) → D_x
22. Polygon(B, E, meanxy, K) → poly_B, B_1, e_1, meanxy_1, k_1
23. Polygon(A, I, meanxy, J) → poly_A, a_1, i_1, meanxy_2, j_1
24. Polygon(meanxy, L, C, G) → poly_C, meanxy_3, l_1, c_1, g_1
25. Polygon(meanxy, M, D, H) → poly_D, meanxy_4, m, d_1, h_1
26. Vector(K, B) → B_y
27. Vector(J, A) → A_y
28. Vector(L, C) → C_y
29. Vector(M, D) → D_y
30. Sum(signedareas) → Sxy
31. Sum(x({A_x, B_x, C_x, D_x})^(2)) → Sxx
32. Sum(y({A_y, B_y, C_y, D_y})^(2)) → Syy
33. OrthogonalLine(F, a) → l
34. OrthogonalLine(N, b) → n
35. Intersect(l, n) → O
36. Polygon(meanxy, N, O, F) → poly1, meanxy_5, n_1, o, f_1
37. Line(P, xAxis) → p
38. Circle(P, Segment[meanxy, J]) → q
39. Intersect(q, p, 2) → Q
40. Circle(Q, Segment[meanxy, K]) → r
41. Intersect(r, p, 2) → R
42. Circle(R, Segment[meanxy, L]) → s
43. Intersect(s, p, 2) → S
44. Circle(S, Segment[meanxy, F]) → t
45. OrthogonalLine(Q, p) → b_1
46. OrthogonalLine(R, p) → m_1
47. OrthogonalLine(S, p) → p_1
48. Polygon(P, Q, 4) → poly2, r_1, s_1, t_1, a_2, U, V
49. Polygon(Q, R, 4) → poly3, b_2, c_2, d_2, e_2, W, Z
50. Polygon(R, S, 4) → poly4, f_2, g_2, h_2, i_2, A_1, C_1
51. Circle(S, Segment[meanxy, M]) → q_1
52. Intersect(q_1, p, 2) → T
53. OrthogonalLine(T, p) → j_2
54. Polygon(S, T, 4) → poly5, k_2, l_2, m_2, n_2, D_1, E_1
55. Circle(P, u) → p_2
56. Intersect(p_2, p) → F_1, G_1
57. Polygon(P, G_1, 4) → poly6, q_2, r_2, s_2, t_2, H_1, I_1
58. OrthogonalLine(P, p) → a_3
59. Circle(P, Segment[meanxy, I]) → c_3
60. Intersect(c_3, a_3, 1) → J_1
61. Circle(J_1, Segment[meanxy, E]) → d_3
62. Intersect(d_3, a_3, 1) → K_1
63. Circle(K_1, Segment[meanxy, G]) → e_3
64. Intersect(e_3, a_3, 1) → L_1
65. Circle(L_1, Segment[meanxy, H]) → f_3
66. Intersect(f_3, a_3, 1) → M_1
67. Polygon(J_1, P, 4) → poly7, b_3, g_3, h_3, i_3, N_1, O_1
68. Polygon(K_1, J_1, 4) → poly8, j_3, k_3, l_3, m_3, P_1, Q_1
69. Polygon(L_1, K_1, 4) → poly9, n_3, p_3, q_3, r_3, R_1, S_1
70. Polygon(M_1, L_1, 4) → poly10, s_3, t_3, a_4, b_4, T_1, U_1
71. Circle(P, v) → c_4
72. Intersect(c_4, a_3) → V_1, W_1
73. Polygon(V_1, P, 4) → poly11, d_4, e_4, f_4, g_4, Z_1, A_3
74. OrthogonalLine(V_1, a_3) → h_4
75. OrthogonalLine(G_1, h_4) → i_4
76. Intersect(h_4, i_4) → B_3
77. Polygon(V_1, B_3, G_1, P) → poly12, v_1, b_5, g_5, p_4
78. OrthogonalLine(A_2, p) → j_4
79. OrthogonalLine(B_2, p) → k_4
80. OrthogonalLine(D_2, p) → l_4
81. OrthogonalLine(C_2, p) → m_4
82. Intersect(p, j_4) → E_2
83. Intersect(p, k_4) → F_2
84. Intersect(p, m_4) → G_2
85. Intersect(p, l_4) → H_2
86. Polygon(V_1, D_2, H_2, P) → poly13, v_2, d_5, h_5, p_5
87. Mirror(V_1, a_3) → I_2
88. Mirror(D_2, a_3) → J_2
89. Mirror(H_2, a_3) → K_2
90. Mirror(P, a_3) → P'
91. Polygon(I_2, J_2, K_2, P') → poly13', i_5, j_5, k_5, p'
92. Segment(C_2, G_2) → n_4
93. Segment(D_2, H_2) → q_4
94. Segment(A_2, E_2) → r_4
95. Segment(B_2, F_2) → s_4
96. Vector((x(P), y(P) - vecax), (x(A_2), y(P) - vecax)) → w
97. Vector((x(A_2), y(P) - vecbx), (x(B_2), y(P) - vecbx)) → u_1
98. Vector((x(B_2), y(P) - veccx), (x(C_2), y(P) - veccx)) → w_1
99. Vector((x(C_2), y(P) - vecdx), (x(D_2), y(P) - vecdx)) → u_2
100. PMCC({A, B, C, D}) → pearcorr