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线性回归与相关系数演示

线性回归与相关系数演示
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2018-07-18 07:10
函数解析几何微积分概率统计几何作图
①本范例演示了如何通过GeoGebra绘制数据点并计算线性回归线及相关系数；②涉及的核心数学概念包括线性回归、相关系数、算术平均、微积分、反射、金字塔；③作图要点提炼自构造摘要，使用了Mean（均值）、OrthogonalLine（垂线）、Intersect（交点）、Segment（线段）、PMCC（相关系数）、Polygon（多边形）、TableText（表格文本）、FitLineY（拟合直线）等命令；④适合高中阶段学习解析几何、概率统计的学生使用。

GeoGebra 命令及参数

  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