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Interpreting Correlation

Interpreting Correlation
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2017-05-24 21:39
Coordinate GeometryProbability & StatisticsOptimizationSlider AnimationGraphing
In collections Resources for New A-level Maths Spec
This example demonstrates how the correlation coefficient (r) changes by manipulating data points, where r measures the strength of correlation between 0 and 1. Key math concepts include correlation coefficient, data point distribution, and linear relationships. It uses GeoGebra commands like Element, Sum, Mean, PointLineSegment, Zip, Sequence, Length, Covariance and objects such as 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. Suitable for high school mathematics education to understand data correlation and its practical applications.

GeoGebra Commands & Parameters

  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