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Interpreting Correlation - the effect of rescaling

Interpreting Correlation - the effect of rescaling
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2017-05-24 21:51
Coordinate GeometryProbability & StatisticsSlider AnimationGraphing
In collections Resources for New A-level Maths Spec
This example demonstrates how rescaling data on separate or both axes affects the correlation coefficient. Key math concepts include correlation, data rescaling, and their impact on scatter plots. It uses GeoGebra commands like Element, Sum, Mean, PointLineSegment, Zip, Sequence, Length, Covariance and objects such as h, d, e, f, 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. Suitable for high school students learning the effects of data rescaling on statistical analysis.

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

AI Drawing Prompt Reference

Draw scatter plots for two sets of data, showing the mean on both axes, and connect the mean points to the data points with line segments of different colors to visualize the changes in data center. First, plot the scatter plots of the original data sets, then calculate and mark the mean points for each set. Next, connect each data point to the mean points with line segments of different colors, representing the deviation of data points from the mean. Finally, adjust the scaling of the data on the horizontal and vertical axes using a slider to observe the changes in the scatter plots and connecting line segments, as well as the movement of the mean points.
The prompt above was compiled from the original drawing commands and is for reference only.