from numpy import *
import numpy as np
import matplotlib.pyplot as plt

plt.close()
fig=plt.figure()
plt.grid(True)
plt.axis([0,10,0,8])

#列出數據
point=[[1,2],[2,3],[3,6],[4,7],[6,5],[7,3],[8,2]]
plt.xlabel("X")
plt.ylabel("Y")

#用于求出矩陣中各點的值
XSum = 0.0
X2Sum = 0.0
X3Sum = 0.0
X4Sum = 0.0
ISum = 0.0
YSum = 0.0
XYSum = 0.0
X2YSum = 0.0


#列出各點的位置
for i in range(0,len(point)):

 xi=point[i][0]
 yi=point[i][1]
 plt.scatter(xi,yi,color="red")
 show_point = "("+ str(xi) +","+ str(yi) + ")"
 plt.text(xi,yi,show_point)

 XSum = XSum+xi
 X2Sum = X2Sum+xi**2
 X3Sum = X3Sum + xi**3
 X4Sum = X4Sum + xi**4
 ISum = ISum+1
 YSum = YSum+yi
 XYSum = XYSum+xi*yi
 X2YSum = X2YSum + xi**2*yi

# 進行矩陣運算
# _mat1 設為 mat1 的逆矩陣
m1=[[ISum,XSum, X2Sum],[XSum, X2Sum, X3Sum],[X2Sum, X3Sum, X4Sum]]
mat1 = np.matrix(m1)
m2=[[YSum], [XYSum], [X2YSum]]
mat2 = np.matrix(m2)
_mat1 =mat1.getI()
mat3 = _mat1*mat2

# 用list來提取矩陣數據
m3=mat3.tolist()
a = m3[0][0]
b = m3[1][0]
c = m3[2][0]
# 繪制回歸線
x = np.linspace(0,10)
y = a + b*x + c*x**2
plt.plot(x,y)
show_line = "y="+str(a)+"+("+str(b)+"x)"+"+("+str(c)+"x2)";
plt.title(show_line)
plt.show()