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Using Correlation Coefficient to Describe Data Relationship Strength

Using Correlation Coefficient to Describe Data Relationship Strength
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2012-06-02 00:06
FunctionCoordinate GeometryProbability & StatisticsGraphing
In collections AP Statistics
This GeoGebra example demonstrates how to fit a line to a scatter plot and compute the Pearson product-moment correlation coefficient (PMCC) to quantitatively describe the strength of the linear relationship between two data sets. Core mathematical concepts include correlation coefficient, linear regression, scatter plots, and strength-of-association interpretation. The construction employs GeoGebra commands such as FitLineY for the regression line, PMCC for the correlation value, Textfield and If for dynamic conditional text, and Polygon, Sequence, Segment, and RotateText for plotting data points, drawing segments, and labeling objects A1 through B19. Suitable for high school statistics and probability courses or introductory college statistics, supporting classroom demonstration and self-paced inquiry into how correlation coefficient values correspond to data scatter tightness.

GeoGebra Commands & Parameters

  1. FitLineY(PointList1) → LineFit
  2. PMCC(PointList1) → CorCoeff
  3. Textfield(A2) → InA2
  4. Textfield(A3) → InA3
  5. Textfield(A4) → InA4
  6. Textfield(A5) → InA5
  7. Textfield(A6) → InA6
  8. Textfield(A7) → InA7
  9. Textfield(A8) → InA8
  10. Textfield(A9) → InA9
  11. Textfield(A10) → InA10
  12. Textfield(A11) → InA11
  13. Textfield(A12) → InA12
  14. Textfield(A13) → InA13
  15. Textfield(A14) → InA14
  16. Textfield(A15) → InA15
  17. Textfield(A16) → InA16
  18. Textfield(A17) → InA17
  19. Textfield(A18) → InA18
  20. Textfield(A19) → InA19
  21. Textfield(A20) → InA20
  22. Textfield(A21) → InA21
  23. Textfield(B2) → InB2
  24. Textfield(B3) → InB3
  25. Textfield(B4) → InB4
  26. Textfield(B5) → InB5
  27. Textfield(B6) → InB6
  28. Textfield(B7) → InB7
  29. Textfield(B8) → InB8
  30. Textfield(B9) → InB9
  31. Textfield(B10) → InB10
  32. Textfield(B11) → InB11
  33. Textfield(B12) → InB12
  34. Textfield(B13) → InB13
  35. Textfield(B14) → InB14
  36. Textfield(B15) → InB15
  37. Textfield(B16) → InB16
  38. Textfield(B17) → InB17
  39. Textfield(B18) → InB18
  40. Textfield(B19) → InB19
  41. Textfield(B20) → InB20
  42. Textfield(B21) → InB21
  43. If(CorVisible, "Hide Correlation Coefficient", "Show Correlation Coefficient") → CorButton
  44. If(LineVisible, "Hide Best Fit Line", "Show Best Fit Line") → LineButton
  45. Polygon((40, y(Corner[1])), Corner[2], Corner[3], (40, y(Corner[4]))) → poly1, a, b, c, d
  46. Sequence(Segment[(41, -1 + 4 * i), (56, -1 + 4 * i)], i, 0, 10) → Linesh1
  47. Sequence(Segment[(41 + 7.5 * i, -1), (41 + 7.5 * i, 47)], i, 0, 2) → Linesv1
  48. Sequence(Segment[(60.5 + 7.5 * i, -1), (60.5 + 7.5 * i, 47)], i, 0, 2) → Linesv2
  49. Sequence(Segment[(60.5, -1 + 4 * i), (75.4, -1 + 4 * i)], i, 0, 10) → Linesh2
  50. Segment((41, 47), (56, 47)) → top1
  51. Segment((60.5, 47), (75.5, 47)) → top2
  52. RotateText("Average test score", 90*°) → SideLegend

AI Drawing Prompt Reference

Draw a coordinate plane with a grid background, plot about twenty data points forming a scatter plot, automatically fit a best‑fit regression line through the points, display the Pearson correlation coefficient value on the chart, and add two toggle buttons to show or hide the correlation coefficient and the regression line; keep the design clean for statistics teaching demonstrations in a clear visual style.
The prompt above was compiled from the original drawing commands and is for reference only.