如何在Python中进行二维回归分析？

首先，我不熟悉Python，我仍然几乎不了解Python代码的机制。但是我需要通过Python做一些统计分析

我试过很多方法想弄明白，但我失败了

• 基本上，我有3个数据数组（假设这些数组是

  X

  ，

  Y

  ，

  Z

  ）
• 我用（

  X

  ，

  Y

  ）和（

  Z

  ，

  Y

  ）做了一些分析，制作散点图，并与数据进行最佳拟合以查看相关性
• №1及№2.这很容易
• 现在我需要从图中看到视图上的边，这是一个结合了

  X

  和

  Z

  的边。所以，我做了一个等式（见下文）

---

现在我无法从方程中找出误差，它是

y=a1*x+a2*z+a3

。我找到了

a1

、

a2

、

a3

的最佳值。然而，并不是错误

---

如何找到

a1

、

a2

、

a3

的“错误”？

下面是一个示例Python代码，它使用scipy.optimize.curve\u拟合曲面，并生成原始数据的三维散点图、错误的三维散点图、曲面图和等高线图。将此更改为使用您自己的数据和函数，您应该这样做

import numpy, scipy
import scipy.optimize
import matplotlib
from mpl_toolkits.mplot3d import  Axes3D
from matplotlib import cm # to colormap 3D surfaces from blue to red
import matplotlib.pyplot as plt

graphWidth = 800 # units are pixels
graphHeight = 600 # units are pixels

# 3D contour plot lines
numberOfContourLines = 16


def SurfacePlot(equationFunc, data, params):
    f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)

    matplotlib.pyplot.grid(True)
    axes = Axes3D(f)

    x_data = data[0]
    y_data = data[1]
    z_data = data[2]

    xModel = numpy.linspace(min(x_data), max(x_data), 20)
    yModel = numpy.linspace(min(y_data), max(y_data), 20)
    X, Y = numpy.meshgrid(xModel, yModel)

    Z = equationFunc(numpy.array([X, Y]), *params)

    axes.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.coolwarm, linewidth=1, antialiased=True)

    axes.scatter(x_data, y_data, z_data) # show data along with plotted surface

    axes.set_title('Surface Plot (click-drag with mouse)') # add a title for surface plot
    axes.set_xlabel('X Data') # X axis data label
    axes.set_ylabel('Y Data') # Y axis data label
    axes.set_zlabel('Z Data') # Z axis data label

    plt.show()
    plt.close('all') # clean up after using pyplot or else thaere can be memory and process problems


def ContourPlot(equationFunc, data, params):
    f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
    axes = f.add_subplot(111)

    x_data = data[0]
    y_data = data[1]
    z_data = data[2]

    xModel = numpy.linspace(min(x_data), max(x_data), 20)
    yModel = numpy.linspace(min(y_data), max(y_data), 20)
    X, Y = numpy.meshgrid(xModel, yModel)

    Z = equationFunc(numpy.array([X, Y]), *params)

    axes.plot(x_data, y_data, 'o')

    axes.set_title('Contour Plot') # add a title for contour plot
    axes.set_xlabel('X Data') # X axis data label
    axes.set_ylabel('Y Data') # Y axis data label

    CS = matplotlib.pyplot.contour(X, Y, Z, numberOfContourLines, colors='k')
    matplotlib.pyplot.clabel(CS, inline=1, fontsize=10) # labels for contours

    plt.show()
    plt.close('all') # clean up after using pyplot or else thaere can be memory and process problems


def ScatterPlot(data, title):
    f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)

    matplotlib.pyplot.grid(True)
    axes = Axes3D(f)
    x_data = data[0]
    y_data = data[1]
    z_data = data[2]

    axes.scatter(x_data, y_data, z_data, depthshade=False, color='k')

    axes.set_title(title)
    axes.set_xlabel('X Data')
    axes.set_ylabel('Y Data')
    axes.set_zlabel('Z Data')

    plt.show()
    plt.close('all') # clean up after using pyplot or else thaere can be memory and process problems


def EquationFunc(data, *params):
    p0 = params[0]
    p1 = params[1]
    return p0 + numpy.sqrt(data[0]) + numpy.cos(data[1] / p1)


if __name__ == "__main__":

    # raw data
    xData = numpy.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0])
    yData = numpy.array([11.0, 12.1, 13.0, 14.1, 15.0, 16.1, 17.0, 18.1, 90.0])
    zData = numpy.array([1.1, 2.2, 3.3, 4.4, 5.5, 6.6, 7.7, 8.0, 9.9])

    pInitial = (1.0, 1.0)
    popt, pcov = scipy.optimize.curve_fit(EquationFunc,(xData,yData),zData, p0=pInitial)

    dataForPlotting = [xData, yData, zData]

    ScatterPlot([xData, yData, zData], 'Data Scatter Plot (click-drag with mouse)')
    SurfacePlot(EquationFunc, [xData, yData, zData], popt)
    ContourPlot(EquationFunc, [xData, yData, zData], popt)

    absError = zData - EquationFunc((xData,yData), *popt)
    ScatterPlot([xData, yData, absError], 'Error Scatter Plot (click-drag with mouse)')

---

您应该使用或建立线性回归。@E.Z.非常感谢您的评论。你能举例说明我的代码吗？那太好了。@E.Z.，谢谢你编辑这个问题。小旁白：对于标题，堆栈溢出的流行样式倾向于句子大小写而不是标题大小写。非常感谢您的帮助。这似乎也很有帮助，但是，我需要从x，z组合的方程中得到误差。这就是为什么我的示例代码计算并绘制误差。谢谢James！实际上，我刚刚开始学习python，所以我可能需要很长时间才能理解您的代码。有没有可能得到错误的方法？或者你能修改一下我的代码吗？如果你能这么做，我想你可以救我的命。非常感谢，在我的示例中，下一行代码计算错误，它是“absError=zData-equalationfunc（（扩展数据，yData），*popt）”

import numpy, scipy
import scipy.optimize
import matplotlib
from mpl_toolkits.mplot3d import  Axes3D
from matplotlib import cm # to colormap 3D surfaces from blue to red
import matplotlib.pyplot as plt

graphWidth = 800 # units are pixels
graphHeight = 600 # units are pixels

# 3D contour plot lines
numberOfContourLines = 16


def SurfacePlot(equationFunc, data, params):
    f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)

    matplotlib.pyplot.grid(True)
    axes = Axes3D(f)

    x_data = data[0]
    y_data = data[1]
    z_data = data[2]

    xModel = numpy.linspace(min(x_data), max(x_data), 20)
    yModel = numpy.linspace(min(y_data), max(y_data), 20)
    X, Y = numpy.meshgrid(xModel, yModel)

    Z = equationFunc(numpy.array([X, Y]), *params)

    axes.plot_surface(X, Y, Z, rstride=1, cstride=1, cmap=cm.coolwarm, linewidth=1, antialiased=True)

    axes.scatter(x_data, y_data, z_data) # show data along with plotted surface

    axes.set_title('Surface Plot (click-drag with mouse)') # add a title for surface plot
    axes.set_xlabel('X Data') # X axis data label
    axes.set_ylabel('Y Data') # Y axis data label
    axes.set_zlabel('Z Data') # Z axis data label

    plt.show()
    plt.close('all') # clean up after using pyplot or else thaere can be memory and process problems


def ContourPlot(equationFunc, data, params):
    f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
    axes = f.add_subplot(111)

    x_data = data[0]
    y_data = data[1]
    z_data = data[2]

    xModel = numpy.linspace(min(x_data), max(x_data), 20)
    yModel = numpy.linspace(min(y_data), max(y_data), 20)
    X, Y = numpy.meshgrid(xModel, yModel)

    Z = equationFunc(numpy.array([X, Y]), *params)

    axes.plot(x_data, y_data, 'o')

    axes.set_title('Contour Plot') # add a title for contour plot
    axes.set_xlabel('X Data') # X axis data label
    axes.set_ylabel('Y Data') # Y axis data label

    CS = matplotlib.pyplot.contour(X, Y, Z, numberOfContourLines, colors='k')
    matplotlib.pyplot.clabel(CS, inline=1, fontsize=10) # labels for contours

    plt.show()
    plt.close('all') # clean up after using pyplot or else thaere can be memory and process problems


def ScatterPlot(data, title):
    f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)

    matplotlib.pyplot.grid(True)
    axes = Axes3D(f)
    x_data = data[0]
    y_data = data[1]
    z_data = data[2]

    axes.scatter(x_data, y_data, z_data, depthshade=False, color='k')

    axes.set_title(title)
    axes.set_xlabel('X Data')
    axes.set_ylabel('Y Data')
    axes.set_zlabel('Z Data')

    plt.show()
    plt.close('all') # clean up after using pyplot or else thaere can be memory and process problems


def EquationFunc(data, *params):
    p0 = params[0]
    p1 = params[1]
    return p0 + numpy.sqrt(data[0]) + numpy.cos(data[1] / p1)


if __name__ == "__main__":

    # raw data
    xData = numpy.array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0])
    yData = numpy.array([11.0, 12.1, 13.0, 14.1, 15.0, 16.1, 17.0, 18.1, 90.0])
    zData = numpy.array([1.1, 2.2, 3.3, 4.4, 5.5, 6.6, 7.7, 8.0, 9.9])

    pInitial = (1.0, 1.0)
    popt, pcov = scipy.optimize.curve_fit(EquationFunc,(xData,yData),zData, p0=pInitial)

    dataForPlotting = [xData, yData, zData]

    ScatterPlot([xData, yData, zData], 'Data Scatter Plot (click-drag with mouse)')
    SurfacePlot(EquationFunc, [xData, yData, zData], popt)
    ContourPlot(EquationFunc, [xData, yData, zData], popt)

    absError = zData - EquationFunc((xData,yData), *popt)
    ScatterPlot([xData, yData, absError], 'Error Scatter Plot (click-drag with mouse)')