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Linear Regression and Correlation Coefficient Demo

Linear Regression and Correlation Coefficient Demo
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2018-07-18 07:10
FunctionCoordinate GeometryCalculusProbability & StatisticsGeometric Construction
This example demonstrates how to plot data points and calculate the linear regression line and correlation coefficient using GeoGebra. It involves core mathematical concepts such as linear regression, correlation coefficient, arithmetic mean, calculus, reflection, and pyramid. Key GeoGebra commands used in the construction include Mean, OrthogonalLine, Intersect, Segment, PMCC, Polygon, TableText, and FitLineY. It is suitable for high school students studying coordinate geometry and probability & statistics.

GeoGebra Commands & Parameters

  1. Mean(B2:B13) → B16
  2. Mean(A2:A13) → A16
  3. OrthogonalLine(A, a) → b
  4. OrthogonalLine(B, a) → c
  5. OrthogonalLine(C, a) → d
  6. OrthogonalLine(D, a) → e
  7. OrthogonalLine(E, a) → f
  8. OrthogonalLine(F, a) → g
  9. OrthogonalLine(G, a) → h
  10. OrthogonalLine(H, a) → i
  11. OrthogonalLine(I, a) → j
  12. OrthogonalLine(J, a) → k
  13. OrthogonalLine(K, a) → l
  14. OrthogonalLine(L, a) → m
  15. Intersect(m, a) → N
  16. Intersect(k, a) → O
  17. Intersect(l, a) → P
  18. Intersect(j, a) → Q
  19. Intersect(h, i) → R
  20. Intersect(a, h) → S
  21. Intersect(h, a) → T
  22. Intersect(g, a) → U
  23. Intersect(f, a) → V
  24. Intersect(e, a) → W
  25. Intersect(d, a) → Z
  26. Intersect(c, a) → A_1
  27. Intersect(b, a) → B_1
  28. Segment(L, N) → n
  29. Segment(J, O) → p
  30. Segment(K, P) → q
  31. Segment(I, Q) → r
  32. OrthogonalLine(H, a) → s
  33. Intersect(s, a) → C_1
  34. Segment(H, C_1) → t
  35. Segment(G, S) → a_1
  36. Segment(F, U) → b_1
  37. Segment(E, V) → c_1
  38. Segment(D, W) → d_1
  39. Segment(C, Z) → e_1
  40. Segment(B, A_1) → f_1
  41. Segment(A, B_1) → g_1
  42. OrthogonalLine(B, h_1) → i_1
  43. OrthogonalLine(C, h_1) → j_1
  44. OrthogonalLine(H, h_1) → k_1
  45. OrthogonalLine(D, h_1) → l_1
  46. OrthogonalLine(E, h_1) → m_1
  47. OrthogonalLine(F, h_1) → n_1
  48. OrthogonalLine(I, h_1) → p_1
  49. OrthogonalLine(A, h_1) → q_1
  50. OrthogonalLine(J, h_1) → r_1
  51. OrthogonalLine(G, h_1) → s_1
  52. OrthogonalLine(K, h_1) → t_1
  53. OrthogonalLine(L, h_1) → a_2
  54. Intersect(i_1, h_1) → D_1
  55. Intersect(j_1, h_1) → E_1
  56. Intersect(l_1, h_1) → F_1
  57. Intersect(m_1, h_1) → G_1
  58. Intersect(n_1, h_1) → H_1
  59. Intersect(k_1, h_1) → I_1
  60. Intersect(p_1, h_1) → J_1
  61. Intersect(q_1, h_1) → K_1
  62. Intersect(r_1, h_1) → L_1
  63. Intersect(s_1, h_1) → M_1
  64. Intersect(t_1, h_1) → N_1
  65. Intersect(a_2, h_1) → O_1
  66. Segment(D_1, B) → b_2
  67. Segment(C, E_1) → c_2
  68. Segment(F_1, D) → d_2
  69. Segment(E, G_1) → e_2
  70. Segment(H_1, F) → f_2
  71. Segment(I, J_1) → g_2
  72. Segment(H, I_1) → h_2
  73. Segment(A, K_1) → i_2
  74. Segment(J, L_1) → j_2
  75. Segment(G, M_1) → k_2
  76. Segment(N_1, K) → l_2
  77. Segment(L, O_1) → m_2
  78. PMCC({A, B, C, D, E, F, G, H, I, J, K, L, M}) → o_1
  79. Polygon(B, (x(B), 0), (0, 0), (0, y(B))) → poly2, b_3, r_2, s_2, t_2
  80. Polygon(C, (x(C), 0), (0, 0), (0, y(C))) → poly3, c_3, d_3, e_3, f_3
  81. Polygon(D, (x(D), 0), (0, 0), (0, y(D))) → poly4, d_4, g_3, h_3, i_3
  82. Polygon(E, (x(E), 0), (0, 0), (0, y(E))) → poly5, e_4, j_3, k_3, l_3
  83. Polygon(F, (x(F), 0), (0, 0), (0, y(F))) → poly6, f_4, m_3, n_3, p_3
  84. Polygon(G, (x(G), 0), (0, 0), (0, y(G))) → poly7, g_4, q_3, r_3, s_3
  85. Polygon(H, (x(H), 0), (0, 0), (0, y(H))) → poly8, h_4, t_3, b_4, c_4
  86. Polygon(I, (x(I), 0), (0, 0), (0, y(I))) → poly9, i_4, j_4, k_4, l_4
  87. Polygon(J, (x(J), 0), (0, 0), (0, y(J))) → poly10, j_5, m_4, n_4, p_4
  88. Polygon(K, (x(K), 0), (0, 0), (0, y(K))) → poly11, k_5, q_4, r_4, s_4
  89. Polygon(L, (x(L), 0), (0, 0), (0, y(L))) → poly12, l_5, t_4, b_5, c_5
  90. Polygon(M, (x(M), 0), (0, 0), (0, y(M))) → poly13, m_5, d_5, e_5, f_5
  91. TableText({{"x", "y", "x-\bar x", "y- \bar y", "(x-\bar x)(y-\bar y", "(x- \bar x)^2", "(y-\bar y)^2"}, {A2, B2, C2, D2, E2, F2, G2}, {A3, B3, C3, D3, E3, F3, G3}, {A4, B4, C4, D4, E4, F4, G4}, {A5, B5, C5, D5, E5, F5, G5}, {A6, B6, C6, D6, E6, F6, G6}, {A7, B7, C7, D7, E7, F7, G7}, {A8, B8, C8, D8, E8, F8, G8}, {A9, B9, C9, D9, E9, F9, G9}, {A10, B10, C10, D10, E10, F10, G10}, {A11, B11, C11, D11, E11, F11, G11}, {A12, B12, C12, D12, E12, F12, G12}, {A13, B13, C13, D13, E13, F13, G13}, {"Total", " ", " ", " ", E14, F14, G14}}, "|_") → text3
  92. TableText({{" ", A21, B21, C21, D21}, {" ", A22, B22, C22, D22}, {" ", A23, B23, C23, D23}, {" ", A24, B24, C24, D24}, {" ", A25, B25, C25, D25}, {" ", A26, B26, C26, D26}, {" ", A27, B27, C27, D27}, {" ", A28, B28, C28, D28}, {" ", A29, B29, C29, D29}, {" ", A30, B30, C30, D30}, {" ", A31, B31, C31, D31}, {" ", A32, B32, C32, D32}, {" ", A33, B33, C33, D33}, {"Total", A34, B34, C34, D34}}, "|_") → text14
  93. FitLineY({A, B, C, D, E, F, G, H, I, J, K, L}) → n_2