线性相关与最小二乘最佳拟合线
几何画板及绘图内容加载中,请稍等……
这个范例演示了线性相关性以及最小二乘法的最佳拟合线。它涉及的核心数学概念包括线性相关、标准差、均值和相关系数。通过使用GeoGebra命令如If、Sequence、MeanY、SampleSDY等,可以构造出数据点的散点图,并通过这些命令计算出最佳拟合线。适合高中数学教学和学习使用。
GeoGebra 命令及参数
If(xvalues ≥ 1, Element[list1, 1], 0) → G4If(xvalues ≥ 2, Element[list1, 2], 0) → G5If(xvalues ≥ 3, Element[list1, 3], 0) → G6If(xvalues ≥ 4, Element[list1, 4], 0) → G7If(xvalues ≥ 5, Element[list1, 5], 0) → G8If(xvalues ≥ 8, Element[list1, 8], 0) → G11If(xvalues ≥ 9, Element[list1, 9], 0) → G12If(xvalues ≥ 10, Element[list1, 10], 0) → G13If(xvalues ≥ 11, Element[list1, 11], 0) → G14If(xvalues ≥ 6, Element[list1, 6], 0) → G9If(xvalues ≥ 7, Element[list1, 7], 0) → G10If(xvalues ≥ 15, Element[list1, 15], 0) → G18If(xvalues ≥ 12, Element[list1, 12], 0) → G15If(xvalues ≥ 13, Element[list1, 13], 0) → G16If(xvalues ≥ 14, Element[list1, 14], 0) → G17If(xvalues ≥ 16, Element[list1, 16], 0) → G19If(xvalues ≥ 17, Element[list1, 17], 0) → G20If(xvalues ≥ 18, Element[list1, 18], 0) → G21If(xvalues ≥ 19, Element[list1, 19], 0) → G22If(xvalues ≥ 20, Element[list1, 20], 0) → G23If(xvalues ≥ 1, Element[list2, 1], 0) → H4If(xvalues ≥ 2, Element[list2, 2], 0) → H5If(xvalues ≥ 3, Element[list2, 3], 0) → H6If(xvalues ≥ 4, Element[list2, 4], 0) → H7If(xvalues ≥ 6, Element[list2, 6], 0) → H9If(xvalues ≥ 7, Element[list2, 7], 0) → H10If(xvalues ≥ 8, Element[list2, 8], 0) → H11If(xvalues ≥ 9, Element[list2, 9], 0) → H12If(xvalues ≥ 10, Element[list2, 10], 0) → H13If(xvalues ≥ 11, Element[list2, 11], 0) → H14If(xvalues ≥ 12, Element[list2, 12], 0) → H15If(xvalues ≥ 13, Element[list2, 13], 0) → H16If(xvalues ≥ 14, Element[list2, 14], 0) → H17If(xvalues ≥ 15, Element[list2, 15], 0) → H18If(xvalues ≥ 16, Element[list2, 16], 0) → H19If(xvalues ≥ 17, Element[list2, 17], 0) → H20If(xvalues ≥ 18, Element[list2, 18], 0) → H21If(xvalues ≥ 19, Element[list2, 19], 0) → H22If(xvalues ≥ 20, Element[list2, 20], 0) → H23If(xvalues ≥ 5, Element[list2, 5], 0) → H8Sequence(Element[list2, j], j, 1, xvalues) → list4MeanY(list5) → meanySequence(Element[list1, i], i, 1, xvalues) → list3SampleSDY(list5) → SyMeanX(list5) → meanxPMCC(list3, list4) → rSampleSDX(list5) → SxSum(F4:F23) → F25If(s1, meanx + "", "\lightgreen{Δ}") → J28If(s2, meany + "", "\lightgreen{Δ}") → J29If(s3, SampleSDX[list5] + "", "\lightgreen{Δ}") → J30If(s4, SampleSDY[list5] + "", "\lightgreen{Δ}") → J31If(s5, r + "", "\lightgreen{Δ}") → J32If(s7, m + "", "\lightgreen{Δ}") → J33If(s6, intercept + "", "\lightgreen{Δ}") → J34TableText({{I28, J28}, {I29, J29}, {I30, J30}, {I31, J31}, {I32, J32}, {I33, J33}, {I34, J34}}, "|_") → text5If(xvalues ≥ 6, Element[list1, 6], 0) → text6If(xvalues ≥ 6, Element[list1, 6], 0) → ""If(xvalues ≥ 4, Element[list2, 4], 0) → text8Textfield(o) → InputBox1Mirror(f, h) → f'Textfield(aa) → InputBox2Max(list1) → xmaxMax(list2) → ymaxmean(B4:B23) → F28mean(C4:C23) → G28SDX(list5) → F29SDY(list5) → G29ResidualPlot({(5, 32), (10, 34), (11, 28), (11, 34), (12, 36), (15, 35), (25, 45), (30, 28), (36, 31), (40, 34), (41, 33), (47, 36), (49, 38), (52, 38), (52, 40), (54, 43), (57, 45), (60, 48), (62, 50), (63, 53)}, FitPoly[{(5, 32), (10, 34), (11, 28), (11, 34), (12, 36), (15, 35), (25, 45), (30, 28), (36, 31), (40, 34), (41, 33), (47, 36), (49, 38), (52, 38), (52, 40), (54, 43), (57, 45), (60, 48), (62, 50), (63, 53)}, 1]) →mean(B4:B23) → B26