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python上的双变量线性回归

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python上的双变量线性回归,python,statistics,linear-regression,statsmodels,Python,Statistics,Linear Regression,Statsmodels,我正在开发一个代码来分析两个变量之间的关系。我使用数据帧将变量保存在两列中，如下所示： column A = 132.54672, 201.3845717, 323.2654551 column B = 51.54671995, 96.38457166, 131.2654551 我曾尝试使用statsmodels，但它说我没有足够的样本 有人能帮我吗？为了计算其他变量，我需要定义系数和截距 y = coefficient * x + intercept 好的，这里有一个使用DataFr

我正在开发一个代码来分析两个变量之间的关系。我使用数据帧将变量保存在两列中，如下所示：

column A = 132.54672, 201.3845717, 323.2654551  
column B = 51.54671995,  96.38457166, 131.2654551
我曾尝试使用statsmodels，但它说我没有足够的样本

有人能帮我吗？为了计算其他变量，我需要定义系数和截距

y = coefficient * x + intercept
好的，这里有一个使用DataFrame的解决方案。我跳过导入命令，只显示相关部分。如果你想知道它们是什么，请给我留言

我使用NumPy的
polyfit
进行1阶线性回归。您可以打印拟合（
fit
）以获得斜率和截距
fit[0]
是截距，
fit[1]
是斜率（或者你所说的系数）

好的，下面是一个使用DataFrame的解决方案。我跳过导入命令，只显示相关部分。如果你想知道它们是什么，请给我留言

我使用NumPy的
polyfit
进行1阶线性回归。您可以打印拟合（
fit
）以获得斜率和截距
fit[0]
是截距，
fit[1]
是斜率（或者你所说的系数）

您可以使用
曲线拟合来实现这一点：


import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit

x = np.array([132.54672, 201.3845717, 323.2654551])
y = np.array([51.54671995, 96.38457166, 131.2654551])

linear = lambda x, a, b: a * x + b

popt, pcov = curve_fit(linear, x, y, p0=[1, 1])
plt.plot(x, y, "rx")
plt.plot(x, linear(x, *popt), "b-")
plt.title("f(x)=a*x+b, a={:.2f}, b={:.2f}".format(*popt))
plt.show()


绘图：


您可以使用
曲线拟合来实现这一点：


import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit

x = np.array([132.54672, 201.3845717, 323.2654551])
y = np.array([51.54671995, 96.38457166, 131.2654551])

linear = lambda x, a, b: a * x + b

popt, pcov = curve_fit(linear, x, y, p0=[1, 1])
plt.plot(x, y, "rx")
plt.plot(x, linear(x, *popt), "b-")
plt.title("f(x)=a*x+b, a={:.2f}, b={:.2f}".format(*popt))
plt.show()


绘图：


除了前面的优秀答案之外，这里还有一个图形装配工，它有一个3D散点图、3D曲面图和一个等高线图


import numpy, scipy, 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(func, data, fittedParameters):
    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 = func(numpy.array([X, Y]), *fittedParameters)

    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(func, data, fittedParameters):
    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 = func(numpy.array([X, Y]), *fittedParameters)

    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):
    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)

    axes.set_title('Scatter Plot (click-drag with mouse)')
    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 func(data, a, alpha, beta):
    t = data[0]
    p_p = data[1]
    return a * (t**alpha) * (p_p**beta)


if __name__ == "__main__":
    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])

    data = [xData, yData, zData]

    initialParameters = [1.0, 1.0, 1.0] # these are the same as scipy default values in this example

    # here a non-linear surface fit is made with scipy's curve_fit()
    fittedParameters, pcov = scipy.optimize.curve_fit(func, [xData, yData], zData, p0 = initialParameters)

    ScatterPlot(data)
    SurfacePlot(func, data, fittedParameters)
    ContourPlot(func, data, fittedParameters)

    print('fitted prameters', fittedParameters)

    modelPredictions = func(data, *fittedParameters) 

    absError = modelPredictions - zData

    SE = numpy.square(absError) # squared errors
    MSE = numpy.mean(SE) # mean squared errors
    RMSE = numpy.sqrt(MSE) # Root Mean Squared Error, RMSE
    Rsquared = 1.0 - (numpy.var(absError) / numpy.var(zData))
    print('RMSE:', RMSE)
    print('R-squared:', Rsquared)



除了前面的优秀答案外，这里还有一个具有3D散点图、3D曲面图和等高线图的图形装配工


import numpy, scipy, 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(func, data, fittedParameters):
    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 = func(numpy.array([X, Y]), *fittedParameters)

    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(func, data, fittedParameters):
    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 = func(numpy.array([X, Y]), *fittedParameters)

    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):
    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)

    axes.set_title('Scatter Plot (click-drag with mouse)')
    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 func(data, a, alpha, beta):
    t = data[0]
    p_p = data[1]
    return a * (t**alpha) * (p_p**beta)


if __name__ == "__main__":
    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])

    data = [xData, yData, zData]

    initialParameters = [1.0, 1.0, 1.0] # these are the same as scipy default values in this example

    # here a non-linear surface fit is made with scipy's curve_fit()
    fittedParameters, pcov = scipy.optimize.curve_fit(func, [xData, yData], zData, p0 = initialParameters)

    ScatterPlot(data)
    SurfacePlot(func, data, fittedParameters)
    ContourPlot(func, data, fittedParameters)

    print('fitted prameters', fittedParameters)

    modelPredictions = func(data, *fittedParameters) 

    absError = modelPredictions - zData

    SE = numpy.square(absError) # squared errors
    MSE = numpy.mean(SE) # mean squared errors
    RMSE = numpy.sqrt(MSE) # Root Mean Squared Error, RMSE
    Rsquared = 1.0 - (numpy.var(absError) / numpy.var(zData))
    print('RMSE:', RMSE)
    print('R-squared:', Rsquared)



使用
scipy.stats
：


import pandas as pd
from scipy import stats
import matplotlib.pyplot as plt


column_A= [132.54672, 201.3845717, 323.2654551]
column_B= [51.54671995, 96.38457166, 131.2654551]
df = pd.DataFrame({'A': column_A, 'B': column_B})

reg = stats.linregress(df.A, df.B)

plt.plot(df.A, df.B, 'bo', label='Data')
plt.plot(df.A, reg.intercept + reg.slope * df.A, 'k-', label='Linear Regression')
plt.xlabel('A')
plt.ylabel('B')
plt.legend()
plt.show()




您还可以从
dir（reg）
中找到有用的方法，其中包括


.intercept


.pvalue


.rvalue


.slope


.stderr


请参阅。
使用
scipy.stats
：


import pandas as pd
from scipy import stats
import matplotlib.pyplot as plt


column_A= [132.54672, 201.3845717, 323.2654551]
column_B= [51.54671995, 96.38457166, 131.2654551]
df = pd.DataFrame({'A': column_A, 'B': column_B})

reg = stats.linregress(df.A, df.B)

plt.plot(df.A, df.B, 'bo', label='Data')
plt.plot(df.A, reg.intercept + reg.slope * df.A, 'k-', label='Linear Regression')
plt.xlabel('A')
plt.ylabel('B')
plt.legend()
plt.show()




您还可以从
dir（reg）
中找到有用的方法，其中包括


.intercept


.pvalue


.rvalue


.slope


.stderr


请参阅。
您的代码是什么？您真的必须使用数据帧吗？X=df['A'].astype（float）Y=df['B'].astype（float）#注意参数顺序model=sm.OLS（Y，X）的差异。fit（）predictions=model.predict（X）#根据模型进行预测#打印统计模型。summary（）我可以使用Arrays请不要在注释中打印代码。改为编辑你的帖子。你的代码是什么？你真的必须使用数据帧吗？X=df['A'].astype（float）Y=df['B'].astype（float）#注意参数顺序model=sm.OLS（Y，X）的差异。fit（）predictions=model.predict（X）#根据模型进行预测#打印统计模型。summary（）我可以使用Arrays请不要在注释中打印代码。改为编辑你的帖子。谢谢！你帮了大忙！我真的很感激@Hugoasisbrandao：如果答案有帮助，你可以标记答案谢谢！你帮了大忙！我真的很感激@Hugoasisbrandao：如果答案有帮助，你可以标记答案