from matplotlib import pyplot as plt

import numpy as np

from mpl_toolkits.mplot3d import Axes3D

fig = plt.figure()

ax = Axes3D(fig)

#列出實驗數據

point=[[2,3,48],[4,5,50],[5,7,51],[8,9,55],[9,12,56]]

plt.xlabel("X1")

plt.ylabel("X2")

#表示矩陣中的值

ISum = 0.0

X1Sum = 0.0

X2Sum = 0.0

X1_2Sum = 0.0

X1X2Sum = 0.0

X2_2Sum = 0.0

YSum = 0.0

X1YSum = 0.0

X2YSum = 0.0

#在圖中顯示各點的位置

for i in range(0,len(point)):

x1i=point[i][0]

x2i=point[i][1]

yi=point[i][2]

ax.scatter(x1i, x2i, yi, color="red")

show_point = "["+ str(x1i) +","+ str(x2i)+","+str(yi) + "]"

ax.text(x1i,x2i,yi,show_point)

ISum = ISum+1

X1Sum = X1Sum+x1i

X2Sum = X2Sum+x2i

X1_2Sum = X1_2Sum+x1i**2

X1X2Sum = X1X2Sum+x1i*x2i

X2_2Sum = X2_2Sum+x2i**2

YSum = YSum+yi

X1YSum = X1YSum+x1i*yi

X2YSum = X2YSum+x2i*yi

# 進行矩陣運算

# _mat1 設為 mat1 的逆矩陣

m1=[[ISum,X1Sum,X2Sum],[X1Sum,X1_2Sum,X1X2Sum],[X2Sum,X1X2Sum,X2_2Sum]]

mat1 = np.matrix(m1)

m2=[[YSum],[X1YSum],[X2YSum]]

mat2 = np.matrix(m2)

_mat1 =mat1.getI()

mat3 = _mat1*mat2

# 用list來提取矩陣數據

m3=mat3.tolist()

a0 = m3[0][0]

a1 = m3[1][0]

a2 = m3[2][0]

# 繪制回歸線

x1 = np.linspace(0,9)

x2 = np.linspace(0,12)

y = a0+a1*x1+a2*x2

ax.plot(x1,x2,y)

show_line = "y="+str(a0)+"+"+str(a1)+"x1"+"+"+str(a2)+"x2"

plt.title(show_line)

plt.show()

總結

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