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Live Regression

Live Regression
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2014-10-17 10:13
Graphing
This example demonstrates how moving data points can affect the linear regression line. Key mathematical concepts include linear regression, correlation coefficient, and residual analysis. Construction involves calculating means, standard deviations, and using GeoGebra commands like MeanX, MeanY, SampleSDY, and ResidualPlot. Suitable for high school students or college freshmen in statistics learning and practice.

GeoGebra Commands & Parameters

  1. MeanX(dataList) → xbar
  2. MeanY(dataList) → ybar
  3. SampleSDY(dataList) → s_y
  4. SampleSDX(dataList) → s_x
  5. PMCC(dataList) → r
  6. ResidualPlot(dataList, f) → residualPoints
  7. Sequence(y(Element[residualPoints, k]), k, 1, 12) → residuals
  8. Element(x(dataList), A1) → B1
  9. Element(y(dataList), A1) → C1
  10. Element(x(dataList), A2) → B2
  11. Element(y(dataList), A2) → C2
  12. Element(x(dataList), A3) → B3
  13. Element(y(dataList), A3) → C3
  14. Element(x(dataList), A4) → B4
  15. Element(y(dataList), A4) → C4
  16. Element(x(dataList), A5) → B5
  17. Element(y(dataList), A5) → C5
  18. Element(x(dataList), A6) → B6
  19. Element(y(dataList), A6) → C6
  20. Element(x(dataList), A7) → B7
  21. Element(y(dataList), A7) → C7
  22. Element(x(dataList), A8) → B8
  23. Element(y(dataList), A8) → C8
  24. Element(x(dataList), A9) → B9
  25. Element(y(dataList), A9) → C9
  26. Element(x(dataList), A10) → B10
  27. Element(y(dataList), A10) → C10
  28. Element(x(dataList), A11) → B11
  29. Element(y(dataList), A11) → C11
  30. Element(x(dataList), A12) → B12
  31. Element(y(dataList), A12) → C12
  32. Sequence(Segment[Element[dataList, k], (x(Element[dataList, k]), f(x(Element[dataList, k])))], k, 1, 12) → residualSegments
  33. Sequence(y(Element[dataList, k]) - g(x(Element[dataList, k])), k, 1, 12) → residualsOfGuess
  34. Sum(residualsOfGuess) → sumOfGuessResiduals
  35. Sequence(Element[residualsOfGuess, k]^(2), k, 1, 12) → squaresOfGuessResiduals
  36. Sum(squaresOfGuessResiduals) → sumOfGuessSquaredResiduals
  37. LaTeX(r, true, true) → text1
  38. Sequence(Element[residuals, k]^(2), k, 1, 12) → squaresOfResiduals
  39. Sum(squaresOfResiduals) → sumOfSquaredResiduals
  40. Sum(residuals) → sumOfResiduals
  41. LaTeX(sumOfGuessSquaredResiduals, true, true) → text2
  42. LaTeX(sumOfSquaredResiduals, true, true) → text3

AI Drawing Prompt Reference

Create a linear regression plot showing how moving data points affects the regression line. Include data points and the fitted line, with mean, standard deviation, and residuals labeled. Use different colors or shapes for residuals, and display the sum of squared residuals and correlation coefficient values. Start with data points and the regression line, then calculate and show residuals and their squares, finally label key statistics.
The prompt above was compiled from the original drawing commands and is for reference only.