线性相关与最小二乘最佳拟合线

线性相关与最小二乘最佳拟合线
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2020-03-15 14:07
这个范例演示了线性相关性以及最小二乘法的最佳拟合线。它涉及的核心数学概念包括线性相关、标准差、均值和相关系数。通过使用GeoGebra命令如If、Sequence、MeanY、SampleSDY等,可以构造出数据点的散点图,并通过这些命令计算出最佳拟合线。适合高中数学教学和学习使用。

GeoGebra 命令及参数

  1. If(xvalues ≥ 1, Element[list1, 1], 0) → G4
  2. If(xvalues ≥ 2, Element[list1, 2], 0) → G5
  3. If(xvalues ≥ 3, Element[list1, 3], 0) → G6
  4. If(xvalues ≥ 4, Element[list1, 4], 0) → G7
  5. If(xvalues ≥ 5, Element[list1, 5], 0) → G8
  6. If(xvalues ≥ 8, Element[list1, 8], 0) → G11
  7. If(xvalues ≥ 9, Element[list1, 9], 0) → G12
  8. If(xvalues ≥ 10, Element[list1, 10], 0) → G13
  9. If(xvalues ≥ 11, Element[list1, 11], 0) → G14
  10. If(xvalues ≥ 6, Element[list1, 6], 0) → G9
  11. If(xvalues ≥ 7, Element[list1, 7], 0) → G10
  12. If(xvalues ≥ 15, Element[list1, 15], 0) → G18
  13. If(xvalues ≥ 12, Element[list1, 12], 0) → G15
  14. If(xvalues ≥ 13, Element[list1, 13], 0) → G16
  15. If(xvalues ≥ 14, Element[list1, 14], 0) → G17
  16. If(xvalues ≥ 16, Element[list1, 16], 0) → G19
  17. If(xvalues ≥ 17, Element[list1, 17], 0) → G20
  18. If(xvalues ≥ 18, Element[list1, 18], 0) → G21
  19. If(xvalues ≥ 19, Element[list1, 19], 0) → G22
  20. If(xvalues ≥ 20, Element[list1, 20], 0) → G23
  21. If(xvalues ≥ 1, Element[list2, 1], 0) → H4
  22. If(xvalues ≥ 2, Element[list2, 2], 0) → H5
  23. If(xvalues ≥ 3, Element[list2, 3], 0) → H6
  24. If(xvalues ≥ 4, Element[list2, 4], 0) → H7
  25. If(xvalues ≥ 6, Element[list2, 6], 0) → H9
  26. If(xvalues ≥ 7, Element[list2, 7], 0) → H10
  27. If(xvalues ≥ 8, Element[list2, 8], 0) → H11
  28. If(xvalues ≥ 9, Element[list2, 9], 0) → H12
  29. If(xvalues ≥ 10, Element[list2, 10], 0) → H13
  30. If(xvalues ≥ 11, Element[list2, 11], 0) → H14
  31. If(xvalues ≥ 12, Element[list2, 12], 0) → H15
  32. If(xvalues ≥ 13, Element[list2, 13], 0) → H16
  33. If(xvalues ≥ 14, Element[list2, 14], 0) → H17
  34. If(xvalues ≥ 15, Element[list2, 15], 0) → H18
  35. If(xvalues ≥ 16, Element[list2, 16], 0) → H19
  36. If(xvalues ≥ 17, Element[list2, 17], 0) → H20
  37. If(xvalues ≥ 18, Element[list2, 18], 0) → H21
  38. If(xvalues ≥ 19, Element[list2, 19], 0) → H22
  39. If(xvalues ≥ 20, Element[list2, 20], 0) → H23
  40. If(xvalues ≥ 5, Element[list2, 5], 0) → H8
  41. Sequence(Element[list2, j], j, 1, xvalues) → list4
  42. MeanY(list5) → meany
  43. Sequence(Element[list1, i], i, 1, xvalues) → list3
  44. SampleSDY(list5) → Sy
  45. MeanX(list5) → meanx
  46. PMCC(list3, list4) → r
  47. SampleSDX(list5) → Sx
  48. Sum(F4:F23) → F25
  49. If(s1, meanx + "", "\lightgreen{Δ}") → J28
  50. If(s2, meany + "", "\lightgreen{Δ}") → J29
  51. If(s3, SampleSDX[list5] + "", "\lightgreen{Δ}") → J30
  52. If(s4, SampleSDY[list5] + "", "\lightgreen{Δ}") → J31
  53. If(s5, r + "", "\lightgreen{Δ}") → J32
  54. If(s7, m + "", "\lightgreen{Δ}") → J33
  55. If(s6, intercept + "", "\lightgreen{Δ}") → J34
  56. TableText({{I28, J28}, {I29, J29}, {I30, J30}, {I31, J31}, {I32, J32}, {I33, J33}, {I34, J34}}, "|_") → text5
  57. If(xvalues ≥ 6, Element[list1, 6], 0) → text6
  58. If(xvalues ≥ 6, Element[list1, 6], 0) → ""
  59. If(xvalues ≥ 4, Element[list2, 4], 0) → text8
  60. Textfield(o) → InputBox1
  61. Mirror(f, h) → f'
  62. Textfield(aa) → InputBox2
  63. Max(list1) → xmax
  64. Max(list2) → ymax
  65. mean(B4:B23) → F28
  66. mean(C4:C23) → G28
  67. SDX(list5) → F29
  68. SDY(list5) → G29
  69. ResidualPlot({(5, 32), (10, 34), (11, 28), (11, 34), (12, 36), (15, 35), (25, 45), (30, 28), (36, 31), (40, 34), (41, 33), (47, 36), (49, 38), (52, 38), (52, 40), (54, 43), (57, 45), (60, 48), (62, 50), (63, 53)}, FitPoly[{(5, 32), (10, 34), (11, 28), (11, 34), (12, 36), (15, 35), (25, 45), (30, 28), (36, 31), (40, 34), (41, 33), (47, 36), (49, 38), (52, 38), (52, 40), (54, 43), (57, 45), (60, 48), (62, 50), (63, 53)}, 1]) →
  70. mean(B4:B23) → B26