Python 實現多元線性回歸預測

一、二元輸入特征線性回歸

測試數據為：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代碼如下：

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

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

#加載數據
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] //根據數據輸入的不同確定是int 還是其他類型
            #5.5277,9.1302
            data.append(current)
    return data

data = load_exdata('ex1data2.txt');
data = np.array(data,np.int64)//根據數據輸入的不同確定是int 還是其他類型


#特征縮放
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])     # 標准差
#     print(mu)
#     print(sigma)
    X_norm  = (X - mu) / sigma
    return X_norm,mu,sigma
 
#計算損失
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)
    # 存儲歷史誤差
    J_history = np.zeros((num_iters, 1))
    for iter in range(num_iters):
        # 對J求導，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  #迭代次數
alpha = 0.01    #學習率
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、多元線性回歸，以三個特征輸入為例

輸入數據：testdata.txt。其中第一列是指輸入的數據序列，不可讀入

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 代碼：

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



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


#加載數據
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)//數據是浮點型


# 特征縮放
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])  # 標准差
    # print(mu)
    #     print(sigma)
    X_norm = (X - mu) / sigma
    return X_norm, mu, sigma


# 計算損失
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)
    # 存儲歷史誤差
    J_history = np.zeros((num_iters, 1))
    for iter in range(num_iters):
        # 對J求導，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  # 迭代次數
alpha = 0.01  # 學習率
x = data[:, ( 1,2,3)].reshape((-1, 3))//數據特征輸入，采用數據集一行的，第1，2，3個數據，然后將其變成一行，所以用shape
y = data[:, 4].reshape((-1, 1))//輸出特征，數據集的第四位
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))//因為x+y.總共有四個輸入，所以theta是四維

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])//輸入為3維