Python 实现多元线性回归预测

一、二元输入特征线性回归

测试数据为：ex1data2.txt

2104,3,399900
1600,3,329900
2400,3,369000
1416,2,232000
3000,4,539900
1985,4,299900
1534,3,314900
1427,3,198999
1380,3,212000
1494,3,242500
1940,4,239999
2000,3,347000
1890,3,329999
4478,5,699900
1268,3,259900
2300,4,449900
1320,2,299900
1236,3,199900
2609,4,499998
3031,4,599000
1767,3,252900
1888,2,255000
1604,3,242900
1962,4,259900
3890,3,573900
1100,3,249900
1458,3,464500
2526,3,469000
2200,3,475000
2637,3,299900
1839,2,349900
1000,1,169900
2040,4,314900
3137,3,579900
1811,4,285900
1437,3,249900
1239,3,229900
2132,4,345000
4215,4,549000
2162,4,287000
1664,2,368500
2238,3,329900
2567,4,314000
1200,3,299000
852,2,179900
1852,4,299900
1203,3,239500

Python代码如下：

#-*- coding: UTF-8 -*-

import random
import numpy as np
import matplotlib.pyplot as plt

#加载数据
def load_exdata(filename):
    data = []
    with open(filename, 'r') as f:
        for line in f.readlines():
            line = line.split(',')
            current = [int(item) for item in line] //根据数据输入的不同确定是int 还是其他类型
            #5.5277,9.1302
            data.append(current)
    return data

data = load_exdata('ex1data2.txt');
data = np.array(data,np.int64)//根据数据输入的不同确定是int 还是其他类型


#特征缩放
def featureNormalize(X):
    X_norm = X;
    mu = np.zeros((1,X.shape[1]))
    sigma = np.zeros((1,X.shape[1]))
    for i in range(X.shape[1]):
        mu[0,i] = np.mean(X[:,i]) # 均值
        sigma[0,i] = np.std(X[:,i])     # 标准差
#     print(mu)
#     print(sigma)
    X_norm  = (X - mu) / sigma
    return X_norm,mu,sigma
 
#计算损失
def computeCost(X, y, theta):
    m = y.shape[0]
#     J = (np.sum((X.dot(theta) - y)**2)) / (2*m)
    C = X.dot(theta) - y
    J2 = (C.T.dot(C))/ (2*m)
    return J2
 
#梯度下降
def gradientDescent(X, y, theta, alpha, num_iters):
    m = y.shape[0]
    #print(m)
    # 存储历史误差
    J_history = np.zeros((num_iters, 1))
    for iter in range(num_iters):
        # 对J求导，得到 alpha/m * (WX - Y)*x(i)， (3,m)*(m,1)  X (m,3)*(3,1) = (m,1)
        theta = theta - (alpha/m) * (X.T.dot(X.dot(theta) - y))
        J_history[iter] = computeCost(X, y, theta)
    return J_history,theta
     
 
iterations = 10000  #迭代次数
alpha = 0.01    #学习率
x = data[:,(0,1)].reshape((-1,2))
y = data[:,2].reshape((-1,1))
m = y.shape[0]
x,mu,sigma = featureNormalize(x)
X = np.hstack([x,np.ones((x.shape[0], 1))])
# X = X[range(2),:]
# y = y[range(2),:]
 
theta = np.zeros((3, 1))
 
j = computeCost(X,y,theta)
J_history,theta = gradientDescent(X, y, theta, alpha, iterations)
 
 
print('Theta found by gradient descent',theta)

def predict(data):
    testx = np.array(data)
    testx = ((testx - mu) / sigma)
    testx = np.hstack([testx,np.ones((testx.shape[0], 1))])
    price = testx.dot(theta)
    print('price is %d ' % (price))
 
predict([1650,3])

二、多元线性回归，以三个特征输入为例

输入数据：testdata.txt。其中第一列是指输入的数据序列，不可读入

1,230.1,37.8,69.2,22.1
2,44.5,39.3,45.1,10.4
3,17.2,45.9,69.3,9.3
4,151.5,41.3,58.5,18.5
5,180.8,10.8,58.4,12.9
6,8.7,48.9,75,7.2
7,57.5,32.8,23.5,11.8
8,120.2,19.6,11.6,13.2
9,8.6,2.1,1,4.8
10,199.8,2.6,21.2,10.6
11,66.1,5.8,24.2,8.6
12,214.7,24,4,17.4
13,23.8,35.1,65.9,9.2
14,97.5,7.6,7.2,9.7
15,204.1,32.9,46,19
16,195.4,47.7,52.9,22.4
17,67.8,36.6,114,12.5
18,281.4,39.6,55.8,24.4
19,69.2,20.5,18.3,11.3
20,147.3,23.9,19.1,14.6
21,218.4,27.7,53.4,18
22,237.4,5.1,23.5,12.5
23,13.2,15.9,49.6,5.6
24,228.3,16.9,26.2,15.5
25,62.3,12.6,18.3,9.7
26,262.9,3.5,19.5,12
27,142.9,29.3,12.6,15
28,240.1,16.7,22.9,15.9
29,248.8,27.1,22.9,18.9
30,70.6,16,40.8,10.5
31,292.9,28.3,43.2,21.4
32,112.9,17.4,38.6,11.9
33,97.2,1.5,30,9.6
34,265.6,20,0.3,17.4
35,95.7,1.4,7.4,9.5
36,290.7,4.1,8.5,12.8
37,266.9,43.8,5,25.4
38,74.7,49.4,45.7,14.7
39,43.1,26.7,35.1,10.1
40,228,37.7,32,21.5
41,202.5,22.3,31.6,16.6
42,177,33.4,38.7,17.1
43,293.6,27.7,1.8,20.7
44,206.9,8.4,26.4,12.9
45,25.1,25.7,43.3,8.5
46,175.1,22.5,31.5,14.9
47,89.7,9.9,35.7,10.6
48,239.9,41.5,18.5,23.2
49,227.2,15.8,49.9,14.8
50,66.9,11.7,36.8,9.7
51,199.8,3.1,34.6,11.4
52,100.4,9.6,3.6,10.7
53,216.4,41.7,39.6,22.6
54,182.6,46.2,58.7,21.2
55,262.7,28.8,15.9,20.2
56,198.9,49.4,60,23.7
57,7.3,28.1,41.4,5.5
58,136.2,19.2,16.6,13.2
59,210.8,49.6,37.7,23.8
60,210.7,29.5,9.3,18.4
61,53.5,2,21.4,8.1
62,261.3,42.7,54.7,24.2
63,239.3,15.5,27.3,15.7
64,102.7,29.6,8.4,14
65,131.1,42.8,28.9,18
66,69,9.3,0.9,9.3
67,31.5,24.6,2.2,9.5
68,139.3,14.5,10.2,13.4
69,237.4,27.5,11,18.9
70,216.8,43.9,27.2,22.3
71,199.1,30.6,38.7,18.3
72,109.8,14.3,31.7,12.4
73,26.8,33,19.3,8.8
74,129.4,5.7,31.3,11
75,213.4,24.6,13.1,17
76,16.9,43.7,89.4,8.7
77,27.5,1.6,20.7,6.9
78,120.5,28.5,14.2,14.2
79,5.4,29.9,9.4,5.3
80,116,7.7,23.1,11
81,76.4,26.7,22.3,11.8
82,239.8,4.1,36.9,12.3
83,75.3,20.3,32.5,11.3
84,68.4,44.5,35.6,13.6
85,213.5,43,33.8,21.7
86,193.2,18.4,65.7,15.2
87,76.3,27.5,16,12
88,110.7,40.6,63.2,16
89,88.3,25.5,73.4,12.9
90,109.8,47.8,51.4,16.7
91,134.3,4.9,9.3,11.2
92,28.6,1.5,33,7.3
93,217.7,33.5,59,19.4
94,250.9,36.5,72.3,22.2
95,107.4,14,10.9,11.5
96,163.3,31.6,52.9,16.9
97,197.6,3.5,5.9,11.7
98,184.9,21,22,15.5
99,289.7,42.3,51.2,25.4
100,135.2,41.7,45.9,17.2
101,222.4,4.3,49.8,11.7
102,296.4,36.3,100.9,23.8
103,280.2,10.1,21.4,14.8
104,187.9,17.2,17.9,14.7
105,238.2,34.3,5.3,20.7
106,137.9,46.4,59,19.2
107,25,11,29.7,7.2
108,90.4,0.3,23.2,8.7
109,13.1,0.4,25.6,5.3
110,255.4,26.9,5.5,19.8
111,225.8,8.2,56.5,13.4
112,241.7,38,23.2,21.8
113,175.7,15.4,2.4,14.1
114,209.6,20.6,10.7,15.9
115,78.2,46.8,34.5,14.6
116,75.1,35,52.7,12.6
117,139.2,14.3,25.6,12.2
118,76.4,0.8,14.8,9.4
119,125.7,36.9,79.2,15.9
120,19.4,16,22.3,6.6
121,141.3,26.8,46.2,15.5
122,18.8,21.7,50.4,7
123,224,2.4,15.6,11.6
124,123.1,34.6,12.4,15.2
125,229.5,32.3,74.2,19.7
126,87.2,11.8,25.9,10.6
127,7.8,38.9,50.6,6.6
128,80.2,0,9.2,8.8
129,220.3,49,3.2,24.7
130,59.6,12,43.1,9.7
131,0.7,39.6,8.7,1.6
132,265.2,2.9,43,12.7
133,8.4,27.2,2.1,5.7
134,219.8,33.5,45.1,19.6
135,36.9,38.6,65.6,10.8
136,48.3,47,8.5,11.6
137,25.6,39,9.3,9.5
138,273.7,28.9,59.7,20.8
139,43,25.9,20.5,9.6
140,184.9,43.9,1.7,20.7
141,73.4,17,12.9,10.9
142,193.7,35.4,75.6,19.2
143,220.5,33.2,37.9,20.1
144,104.6,5.7,34.4,10.4
145,96.2,14.8,38.9,11.4
146,140.3,1.9,9,10.3
147,240.1,7.3,8.7,13.2
148,243.2,49,44.3,25.4
149,38,40.3,11.9,10.9
150,44.7,25.8,20.6,10.1
151,280.7,13.9,37,16.1
152,121,8.4,48.7,11.6
153,197.6,23.3,14.2,16.6
154,171.3,39.7,37.7,19
155,187.8,21.1,9.5,15.6
156,4.1,11.6,5.7,3.2
157,93.9,43.5,50.5,15.3
158,149.8,1.3,24.3,10.1
159,11.7,36.9,45.2,7.3
160,131.7,18.4,34.6,12.9
161,172.5,18.1,30.7,14.4
162,85.7,35.8,49.3,13.3
163,188.4,18.1,25.6,14.9
164,163.5,36.8,7.4,18
165,117.2,14.7,5.4,11.9
166,234.5,3.4,84.8,11.9
167,17.9,37.6,21.6,8
168,206.8,5.2,19.4,12.2
169,215.4,23.6,57.6,17.1
170,284.3,10.6,6.4,15
171,50,11.6,18.4,8.4
172,164.5,20.9,47.4,14.5
173,19.6,20.1,17,7.6
174,168.4,7.1,12.8,11.7
175,222.4,3.4,13.1,11.5
176,276.9,48.9,41.8,27
177,248.4,30.2,20.3,20.2
178,170.2,7.8,35.2,11.7
179,276.7,2.3,23.7,11.8
180,165.6,10,17.6,12.6
181,156.6,2.6,8.3,10.5
182,218.5,5.4,27.4,12.2
183,56.2,5.7,29.7,8.7
184,287.6,43,71.8,26.2
185,253.8,21.3,30,17.6
186,205,45.1,19.6,22.6
187,139.5,2.1,26.6,10.3
188,191.1,28.7,18.2,17.3
189,286,13.9,3.7,15.9
190,18.7,12.1,23.4,6.7
191,39.5,41.1,5.8,10.8
192,75.5,10.8,6,9.9
193,17.2,4.1,31.6,5.9
194,166.8,42,3.6,19.6
195,149.7,35.6,6,17.3
196,38.2,3.7,13.8,7.6
197,94.2,4.9,8.1,9.7
198,177,9.3,6.4,12.8
199,283.6,42,66.2,25.5
200,232.1,8.6,8.7,13.4

python 代码：

#-*- coding: UTF-8 -*-



import random
import numpy as np
import matplotlib.pyplot as plt


#加载数据
def load_exdata(filename):
    data = []
    with open(filename, 'r') as f:
        for line in f.readlines():
            line = line.split(',')
            current = [float(item) for item in line]
            #5.5277,9.1302
            data.append(current)
    return data

data = load_exdata('testdata.txt');
data = np.array(data,np.float64)//数据是浮点型


# 特征缩放
def featureNormalize(X):
    X_norm = X;
    mu = np.zeros((1, X.shape[1]))
    sigma = np.zeros((1, X.shape[1]))
    for i in range(X.shape[1]):
        mu[0, i] = np.mean(X[:, i])  # 均值
        sigma[0, i] = np.std(X[:, i])  # 标准差
    # print(mu)
    #     print(sigma)
    X_norm = (X - mu) / sigma
    return X_norm, mu, sigma


# 计算损失
def computeCost(X, y, theta):
    m = y.shape[0]
    #     J = (np.sum((X.dot(theta) - y)**2)) / (2*m)
    C = X.dot(theta) - y
    J2 = (C.T.dot(C)) / (2 * m)
    return J2


# 梯度下降
def gradientDescent(X, y, theta, alpha, num_iters):
    m = y.shape[0]
    # print(m)
    # 存储历史误差
    J_history = np.zeros((num_iters, 1))
    for iter in range(num_iters):
        # 对J求导，得到 alpha/m * (WX - Y)*x(i)， (3,m)*(m,1)  X (m,3)*(3,1) = (m,1)
        theta = theta - (alpha / m) * (X.T.dot(X.dot(theta) - y))
        J_history[iter] = computeCost(X, y, theta)
    return J_history, theta


iterations = 10000  # 迭代次数
alpha = 0.01  # 学习率
x = data[:, ( 1,2,3)].reshape((-1, 3))//数据特征输入，采用数据集一行的，第1，2，3个数据，然后将其变成一行，所以用shape
y = data[:, 4].reshape((-1, 1))//输出特征，数据集的第四位
m = y.shape[0]
x, mu, sigma = featureNormalize(x)
X = np.hstack([x, np.ones((x.shape[0], 1))])
# X = X[range(2),:]
# y = y[range(2),:]

theta = np.zeros((4, 1))//因为x+y.总共有四个输入，所以theta是四维

j = computeCost(X, y, theta)
J_history, theta = gradientDescent(X, y, theta, alpha, iterations)

print('Theta found by gradient descent', theta)


def predict(data):
    testx = np.array(data)
    testx = ((testx - mu) / sigma)
    testx = np.hstack([testx, np.ones((testx.shape[0], 1))])
    price = testx.dot(theta)
    print('predit value is %f ' % (price))

predict([151.5,41.3,58.5])//输入为3维