回归分析与数据点移动实验

回归分析与数据点移动实验
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2014-10-17 10:13
本范例演示如何通过移动数据点来探究线性回归线的影响。核心数学概念包括线性回归、相关系数、残差分析等。作图要点涉及计算均值、标准差、相关系数,并使用GeoGebra命令如MeanX、MeanY、SampleSDY、ResidualPlot等。适合高中生或大学低年级学生用于统计学学习与实践。

GeoGebra 命令及参数

  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 绘图提示语参考

画一个线性回归图,展示数据点移动如何影响回归线。包含数据点和拟合的直线,并标注均值、标准差和残差。用不同颜色或形状区分残差,并显示残差平方和与相关系数的数值。先画出数据点和回归线,再计算并展示残差及其平方和,最后标注关键统计量。
以上提示语为根据原始绘图命令整理而来,仅供参考。