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Correlation with Same Standard Deviation

Correlation with Same Standard Deviation
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2015-04-06 13:27
Coordinate GeometryProbability & Statistics
When X and Y values come from the same data set, their standard deviations are equal. This example uses GeoGebra to demonstrate this and explore the meaning of the correlation coefficient. Commands used include Point, Mirror, FitLineY, MeanX, OrthogonalLine, PMCC, Segment, RectanglefromDiagonal, If, etc. Suitable for high school math education to help students understand the concepts of correlation and standard deviation.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Mirror(A, y = x) → A'
  3. Point(xAxis) → E
  4. Mirror(E, y = x) → E'
  5. Point(xAxis) → D
  6. Mirror(D, y = x) → D'
  7. Point(xAxis) → C
  8. Mirror(C, y = x) → C'
  9. Point(xAxis) → B
  10. Mirror(B, y = x) → B'
  11. Point({(x(E), y(A')), (x(E), y(B')), (x(E), y(C')), (x(E), y(D')), (x(E), y(E'))}) → K
  12. Point({(x(D), y(A')), (x(D), y(B')), (x(D), y(C')), (x(D), y(D')), (x(D), y(E'))}) → J
  13. Point({(x(C), y(A')), (x(C), y(B')), (x(C), y(C')), (x(C), y(D')), (x(C), y(E'))}) → I
  14. Point({(x(B), y(A')), (x(B), y(B')), (x(B), y(C')), (x(B), y(D')), (x(B), y(E'))}) → H
  15. Point({(x(A), y(A')), (x(A), y(B')), (x(A), y(C')), (x(A), y(D')), (x(A), y(E'))}) → G
  16. FitLineY({G, H, I, J, K}) → b
  17. MeanX({A, B, C, D, E}) → a
  18. OrthogonalLine(F, yAxis) → l
  19. PMCC({G, H, I, J, K}) → c
  20. OrthogonalLine(F, xAxis) → m
  21. Segment(G, H) → d
  22. Segment(G, I) → e
  23. Segment(G, J) → f
  24. Segment(G, K) → g
  25. Segment(H, I) → h
  26. Segment(H, J) → i
  27. Segment(H, K) → j
  28. Segment(I, J) → k
  29. Segment(I, K) → n
  30. Segment(J, K) → p
  31. RectanglefromDiagonal(F, G) → poly1
  32. RectanglefromDiagonal(F, H) → poly2
  33. RectanglefromDiagonal(F, I) → poly3
  34. RectanglefromDiagonal(F, J) → poly4
  35. RectanglefromDiagonal(F, K) → poly5
  36. If(valid, Text["Correlation: " + c, true], Text["Invalid Points: Drag the diamonds up or down to unique y-values."]) → text3