在Python上具有兩個變量的線性回歸

Question

我正在開發代碼來分析兩個變量的關系。 我正在使用DataFrame將變量保存在兩列中，如下所示：

column A = 132.54672, 201.3845717, 323.2654551  
column B = 51.54671995,  96.38457166, 131.2654551

我嘗試使用statsmodels，但是它說我沒有足夠的樣本。

誰能幫我？ 我需要定義系數和截距才能計算其他變量。

y = coefficient * x + intercept

Answer 1

好的，這是使用DataFrame的解決方案。 我跳過了導入命令，只顯示了相關部分。 如果您想知道它們是什么，請給我評論。

我正在使用NumPy的polyfit進行1階線性回歸。您可以打印fit（ fit ）以獲取斜率和截距。 fit[0]是截距， fit[1]是斜率（或系數，如您所稱）

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})

fit = np.poly1d(np.polyfit(df['A'], df['B'], 1))

A_mesh = np.linspace(min(df['A']), max(df['A']), 100)

plt.plot(df['A'], df['B'], 'bx', label='Data', ms=10)
plt.plot(A_mesh, fit(A_mesh), '-b', label='Linear fit')

print (fit)
# 0.4028 x + 4.833

Answer 2

您可以使用curve_fit做到這curve_fit ：

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()

情節：

Answer 3

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()

您還可以從dir(reg)找到有用的方法，其中包括

.intercept .pvalue .rvalue .slope .stderr

看這里 。

Answer 4

除了以前的出色答案之外，這里還有一個圖形擬合器，它具有3D散點圖，3D表面圖和輪廓圖。

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)