線性回歸的求解方法是最小二乘法，具體原理：
保證所有數(shù)據(jù)偏差的平方和最小

Paste_Image.png

Paste_Image.png

Paste_Image.png

證明步驟

損失函數(shù)：

Paste_Image.png

化簡(jiǎn)

Paste_Image.png

Paste_Image.png

Paste_Image.png

對(duì)L求偏導(dǎo)數(shù)

Paste_Image.png

Paste_Image.png

Paste_Image.png

from numpy import *
import matplotlib.pyplot as plt

#1. Get data from file
def load_data_set(filename):
    num_feat = len(open(filename).readline().split('\t')) -1
    data_mat = []
    label_mat = []
    fr = open(filename)
    for line in fr.readlines():
        line_arr = []
        cur_line = line.strip().split('\t')
        for i in range(num_feat):
            line_arr.append(float(cur_line[i]))
        data_mat.append(line_arr)
        label_mat.append(line_arr[-1])
    return data_mat, label_mat

# 2. Get w of function coefficient
def stand_regres(x_arr, y_arr):
    x_mat = mat(x_arr)
    y_mat = mat(y_arr)
    xTx = x_mat.T*x_mat
    # is can inverse
    if linalg.det(xTx) == 0.0:
        print "this matrix is singular, cannot do inverse!!!"
        return
    ws = xTx.I * (x_mat.T*y_mat)
    return ws

xArr, yArr = load_data_set('ext0.txt')
ws = stand_regres(xArr, xArr)
print ws
xMat = mat(xArr)
yMat = mat(yArr)
xCopy = xMat.copy()
xCopy.sort(0)
yHat = xCopy*ws

fig = plt.figure()
# 1 row 1 col the 1 block
ax = fig.add_subplot(111)
# must array
ax.scatter(xMat[:, 1].flatten().A[0], yMat.T[:, 0].flatten().A[0])

ax.plot(xCopy[:, 1], yHat)
plt.show()

```