回归分析与数据点移动实验
几何画板及绘图内容加载中,请稍等……
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
MeanX(dataList) → xbarMeanY(dataList) → ybarSampleSDY(dataList) → s_ySampleSDX(dataList) → s_xPMCC(dataList) → rResidualPlot(dataList, f) → residualPointsSequence(y(Element[residualPoints, k]), k, 1, 12) → residualsElement(x(dataList), A1) → B1Element(y(dataList), A1) → C1Element(x(dataList), A2) → B2Element(y(dataList), A2) → C2Element(x(dataList), A3) → B3Element(y(dataList), A3) → C3Element(x(dataList), A4) → B4Element(y(dataList), A4) → C4Element(x(dataList), A5) → B5Element(y(dataList), A5) → C5Element(x(dataList), A6) → B6Element(y(dataList), A6) → C6Element(x(dataList), A7) → B7Element(y(dataList), A7) → C7Element(x(dataList), A8) → B8Element(y(dataList), A8) → C8Element(x(dataList), A9) → B9Element(y(dataList), A9) → C9Element(x(dataList), A10) → B10Element(y(dataList), A10) → C10Element(x(dataList), A11) → B11Element(y(dataList), A11) → C11Element(x(dataList), A12) → B12Element(y(dataList), A12) → C12Sequence(Segment[Element[dataList, k], (x(Element[dataList, k]), f(x(Element[dataList, k])))], k, 1, 12) → residualSegmentsSequence(y(Element[dataList, k]) - g(x(Element[dataList, k])), k, 1, 12) → residualsOfGuessSum(residualsOfGuess) → sumOfGuessResidualsSequence(Element[residualsOfGuess, k]^(2), k, 1, 12) → squaresOfGuessResidualsSum(squaresOfGuessResiduals) → sumOfGuessSquaredResidualsLaTeX(r, true, true) → text1Sequence(Element[residuals, k]^(2), k, 1, 12) → squaresOfResidualsSum(squaresOfResiduals) → sumOfSquaredResidualsSum(residuals) → sumOfResidualsLaTeX(sumOfGuessSquaredResiduals, true, true) → text2LaTeX(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。