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理解相关系数

理解相关系数
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2017-05-24 21:39
解析几何概率统计最值优化滑块动画函数图像
所属专题 Resources for New A-level Maths Spec
①本范例通过操作数据点，演示相关系数（r）如何变化，r是衡量相关强度的指标（0到1之间）；②涉及核心数学概念：相关系数、数据点分布、线性关系；③作图要点：使用了GeoGebra命令如Element, Sum, Mean, PointLineSegment, Zip, Sequence, Length, Covariance，以及对象J, I, H, G, F, E, D, C, B, A, list2, E2, list1, C2, B2, C5, B5, C11, B11, C10, B10, C9, B9, C8, B8, C7, B7, C6, B6, C4, B4, C3, B3, A1, B1, C1, A3, A4, A5, A6；④适合高中数学教学，用于理解数据相关性及其实际应用。

GeoGebra 命令及参数

  1. Element(list2, 1) → E2
  2. Sum(H2:H11) → H12
  3. Element(list1, 1) → D2
  4. Element(list1, 3) → D4
  5. Element(list1, 4) → D5
  6. Element(list1, 5) → D6
  7. Element(list1, 6) → D7
  8. Element(list1, 7) → D8
  9. Element(list1, 8) → D9
  10. Element(list1, 9) → D10
  11. Element(list1, 10) → D11
  12. Element(list2, 2) → E3
  13. Element(list2, 3) → E4
  14. Element(list2, 4) → E5
  15. Element(list2, 5) → E6
  16. Element(list2, 6) → E7
  17. Element(list2, 7) → E8
  18. Element(list2, 8) → E9
  19. Element(list2, 9) → E10
  20. Element(list2, 10) → E11
  21. Mean(D2:D11) → D12
  22. Mean(E2:E11) → E12
  23. PointLineSegment(b, J) → g
  24. PointLineSegment(b, F) → i
  25. PointLineSegment(b, H) → k
  26. PointLineSegment(b, G) → l
  27. PointLineSegment(b, E) → m
  28. PointLineSegment(b, D) → n
  29. PointLineSegment(b, I) → p
  30. PointLineSegment(b, C) → q
  31. PointLineSegment(b, B) → r
  32. PointLineSegment(b, A) → s
  33. PointLineSegment(c, E) → t
  34. PointLineSegment(c, H) → a_1
  35. PointLineSegment(c, F) → b_1
  36. PointLineSegment(c, G) → c_1
  37. PointLineSegment(c, J) → d_1
  38. PointLineSegment(c, I) → e_1
  39. PointLineSegment(c, D) → f_1
  40. PointLineSegment(c, C) → g_1
  41. PointLineSegment(c, B) → h_1
  42. PointLineSegment(c, A) → i_1
  43. Zip((a, b), a, list1, b, list2) → list3
  44. Sequence(If[(x(Element[list3, i]) < Mean[list1]) ∧ (y(Element[list3, i]) < Mean[list2]), ((x(Element[list3, i]) - Mean[list1]) * (y(Element[list3, i]) - Mean[list2])), 0], i, 1, Length[list1]) → list4
  45. Sequence(If[(x(Element[list3, i]) > Mean[list1]) ∧ (y(Element[list3, i]) > Mean[list2]), ((x(Element[list3, i]) - Mean[list1]) * (y(Element[list3, i]) - Mean[list2])), 0], i, 1, Length[list1]) → list5
  46. Sequence(If[(x(Element[list3, i]) < Mean[list1]) ∧ (y(Element[list3, i]) > Mean[list2]), ((x(Element[list3, i]) - Mean[list1]) * (y(Element[list3, i]) - Mean[list2])), 0], i, 1, Length[list1]) → list6
  47. Sequence(If[(x(Element[list3, i]) > Mean[list1]) ∧ (y(Element[list3, i]) < Mean[list2]), ((x(Element[list3, i]) - Mean[list1]) * (y(Element[list3, i]) - Mean[list2])), 0], i, 1, Length[list1]) → list7
  48. Element(list1, 2) → D3
  49. Length(H2:H11) → H13
  50. Covariance(list3) → a