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线性回归与随机数据集

线性回归与随机数据集
几何画板及绘图内容加载中，请稍等……
2014-05-16 05:17
函数解析几何概率统计几何作图
所属专题 GGBChat4: Statistics 1 ggbchat #4 July 16 2014
①本范例演示了如何通过随机生成的数据点进行线性回归分析；②涉及的核心数学概念包括线性回归、数据拟合、统计概率；③作图要点提炼自构造摘要，使用了Random（随机生成点）、Line（绘制直线）、Intersect（交点计算）、Polygon（多边形）、Vector（向量）、RSquare（决定系数）、SampleSD（样本标准差）、Median（中位数）、FitLineY（拟合直线）、Circle（圆）、Text（文本）等GeoGebra命令和对象；④适合高中数学或统计学课程，用于教学线性回归模型和数据可视化。

GeoGebra 命令及参数

  1. Random(1, 20) → A2
  2. Random(1, 20) → A1
  3. Random(1, 20) → A3
  4. Random(1, 20) → A4
  5. Random(1, 20) → A5
  6. Random(1, 20) → A6
  7. Random(1, 20) → A7
  8. Random(1, 20) → A8
  9. Random(1, 20) → A9
  10. Random(1, 20) → A10
  11. Random(1, 20) → A11
  12. Random(1, 20) → A12
  13. Random(1, 20) → A13
  14. Random(1, 20) → A14
  15. Random(1, 20) → A15
  16. Random(1, 20) → A16
  17. Random(1, 20) → A17
  18. Random(1, 20) → A18
  19. Random(1, 20) → A19
  20. Random(1, 20) → A20
  21. Random(-2, 2) → slope_1
  22. Line(U, V) → line_{guess}
  23. Line(A, x = 0) → a
  24. Line(B, x = 0) → b
  25. Line(C, x = 0) → c
  26. Line(D, x = 0) → d
  27. Line(E, x = 0) → e
  28. Line(F, x = 0) → f
  29. Line(G, x = 0) → g
  30. Line(H, x = 0) → h
  31. Line(I, x = 0) → i
  32. Line(J, x = 0) → j
  33. Line(K, x = 0) → k
  34. Line(L, x = 0) → l
  35. Line(M, x = 0) → m
  36. Line(N, x = 0) → n
  37. Line(NP, x = 0) → np
  38. Line(O, x = 0) → p
  39. Line(P, x = 0) → q
  40. Line(R, x = 0) → s
  41. Line(S, x = 0) → t
  42. Intersect(line_{guess}, a) → A'
  43. Intersect(line_{guess}, b) → B'
  44. Intersect(line_{guess}, c) → C'
  45. Intersect(line_{guess}, d) → D'
  46. Intersect(line_{guess}, e) → E'
  47. Intersect(line_{guess}, f) → F'
  48. Intersect(line_{guess}, g) → G'
  49. Intersect(line_{guess}, h) → H'
  50. Intersect(line_{guess}, i) → I'
  51. Intersect(line_{guess}, j) → J'
  52. Intersect(line_{guess}, k) → K'
  53. Intersect(line_{guess}, l) → L'
  54. Intersect(line_{guess}, m) → M'
  55. Intersect(line_{guess}, n) → N'
  56. Intersect(line_{guess}, np) → NP'
  57. Intersect(line_{guess}, p) → O'
  58. Intersect(line_{guess}, q) → P'
  59. Intersect(line_{guess}, s) → R'
  60. Intersect(line_{guess}, t) → S'
  61. Line(Q, x = 0) → r
  62. Intersect(line_{guess}, r) → Q'
  63. Polygon(A', A, 4) → poly1, a_1, b_1, c_1, d_1, T, W
  64. Polygon(B', B, 4) → poly2, e_1, f_1, g_1, h_1, Z, A_1
  65. Polygon(D', D, 4) → poly3, i_1, j_1, k_1, l_1, B_1, C_1
  66. Polygon(E', E, 4) → poly4, m_1, n_1, p_1, q_1, D_1, E_1
  67. Polygon(C', C, 4) → poly5, r_1, s_1, t_1, a_2, F_1, G_1
  68. Polygon(F', F, 4) → poly6, b_2, c_2, d_2, e_2, H_1, I_1
  69. Polygon(G', G, 4) → poly7, f_2, g_2, h_2, i_2, J_1, K_1
  70. Polygon(H', H, 4) → poly8, j_2, k_2, l_2, m_2, L_1, M_1
  71. Polygon(I', I, 4) → poly9, n_2, p_2, q_2, r_2, N_1, O_1
  72. Polygon(J', J, 4) → poly10, s_2, t_2, a_3, b_3, P_1, Q_1
  73. Polygon(K', K, 4) → poly11, c_3, d_3, e_3, f_3, R_1, S_1
  74. Polygon(L', L, 4) → poly12, g_3, h_3, i_3, j_3, T_1, U_1
  75. Polygon(M', M, 4) → poly13, k_3, l_3, m_3, n_3, V_1, W_1
  76. Polygon(N', N, 4) → poly14, p_3, q_3, r_3, s_3, Z_1, A_2
  77. Polygon(NP', NP, 4) → poly15, t_3, a_4, b_4, c_4, B_2, C_2
  78. Polygon(P', P, 4) → poly16, d_4, e_4, f_4, g_4, D_2, E_2
  79. Polygon(O', O, 4) → poly17, h_4, i_4, j_4, k_4, F_2, G_2
  80. Polygon(Q', Q, 4) → poly18, l_4, m_4, n_4, p_4, H_2, I_2
  81. Polygon(R', R, 4) → poly19, q_4, r_4, s_4, t_4, J_2, K_2
  82. Polygon(S', S, 4) → poly20, a_5, b_5, c_5, d_5, L_2, M_2
  83. Vector((x(A), 0), (x(A), y(A) - y(A'))) → V_A
  84. Vector((x(B), 0), (x(B), y(B) - y(B'))) → V_B
  85. Vector((x(C), 0), (x(C), y(C) - y(C'))) → V_C
  86. Vector((x(D), 0), (x(D), y(D) - y(D'))) → V_D
  87. Vector((x(E), 0), (x(E), y(E) - y(E'))) → V_E
  88. Vector((x(F), 0), (x(F), y(F) - y(F'))) → V_F
  89. Vector((x(G), 0), (x(G), y(G) - y(G'))) → V_G
  90. Vector((x(H), 0), (x(H), y(H) - y(H'))) → V_H
  91. Vector((x(I), 0), (x(I), y(I) - y(I'))) → V_I
  92. Vector((x(J), 0), (x(J), y(J) - y(J'))) → V_J
  93. Vector((x(K), 0), (x(K), y(K) - y(K'))) → V_K
  94. Vector((x(L), 0), (x(L), y(L) - y(L'))) → V_L
  95. Vector((x(M), 0), (x(M), y(M) - y(M'))) → V_M
  96. Vector((x(N), 0), (x(N), y(N) - y(N'))) → V_N
  97. Vector((x(NP), 0), (x(NP), y(NP) - y(NP'))) → V_{NP}
  98. Vector((x(P), 0), (x(P), y(P) - y(P'))) → V_P
  99. Vector((x(Q), 0), (x(Q), y(Q) - y(Q'))) → V_Q
  100. Vector((x(R), 0), (x(R), y(R) - y(R'))) → V_R
  101. Vector((x(O), 0), (x(O), y(O) - y(O'))) → V_O
  102. Vector((x(S), 0), (x(S), y(S) - y(S'))) → V_S
  103. RSquare(data, line_{guess}) → Strength
  104. SampleSD(list_y) → SD_y
  105. Median(list_x) → Median_x
  106. FitLineY(data) → line_{actual}
  107. Circle(((Median_x * 1.5), (2 * SD_y)), (Strength * Max[list_y] / 6)) → CorrelationCircle
  108. Circle(((Median_x * 1.5), (2 * SD_y)), (Strength * Max[list_y] / 6)) → CorrelationCircle_1
  109. Random(-10, 10) → yint_1
  110. Vector((Min[list_x] - 2, 0), (Min[list_x] - 2, over)) → Vector_{over}
  111. Vector((Min[list_x] - 2, 0), (Min[list_x] - 2, (-under))) → Vector_{under}
  112. Text(((Strength * 100) * "%"), (Max[list_x] + 2, 0)) → text1

AI 绘图提示语参考

生成一个随机数据集，用点表示，然后绘制这些点的散点图。接着，根据这些点拟合一条最佳直线，并显示这条直线。再绘制几条垂直于x轴的线，分别从每个点到x轴的交点。最后，在这些交点处标注数据点的值，并添加一些统计信息，如图的标题和坐标轴标签。
以上提示语为根据原始绘图命令整理而来，仅供参考。