机器学习之线性回归预测销量

背景：给出广告在TV,Radio,Newspaper的销售额，利用线性回归预测其以后的销量趋势

数据：

	TV	Radio	Newspaper	Sales
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

#!/usr/bin/python
# -*- coding:utf-8 -*-
import csv
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
import pandas as pd
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression,Ridge
from pprint import pprint

if __name__ == "__main__":
    path = 'Advertising.csv'
    # # 手写读取数据
    # f = file(path)
    # x = []
    # y = []
    # for i, d in enumerate(f):
    #     if i == 0:
    #         continue
    #     d = d.strip()
    #     if not d:
    #         continue
    #     d = map(float, d.split(','))
    #     x.append(d[1:-1])
    #     y.append(d[-1])
    # pprint(x)
    # pprint(y)
    # x = np.array(x)
    # y = np.array(y)

    # Python自带库
    # f = file(path, 'r')
    # print f
    # d = csv.reader(f)
    # for line in d:
    #     print line
    # f.close()

    # # numpy读入
    # p = np.loadtxt(path, delimiter=',', skiprows=1)
    # print p
    # print '\n\n===============\n\n'

    # pandas读入
    data = pd.read_csv(path)    # TV、Radio、Newspaper、Sales读取数据
    x = data[['TV', 'Radio', 'Newspaper']]
    # x = data[['TV', 'Radio']]
    y = data['Sales']
    print x
    print y

    mpl.rcParams['font.sans-serif'] = [u'simHei']#指定默认字体
    mpl.rcParams['axes.unicode_minus'] = False#解决保存图像是负号'-'显示为方块的问题

    # 绘制1，主要目的：看着三组数据的分布情况
    plt.figure(facecolor='w')#画布颜色为白色
    plt.plot(data['TV'], y, 'ro', label='TV')
    plt.plot(data['Radio'], y, 'g^', label='Radio')
    plt.plot(data['Newspaper'], y, 'mv', label='Newspaer')
    plt.legend(loc='lower right')#图例在右下方
    plt.xlabel(u'广告花费', fontsize=16)
    plt.ylabel(u'销售额', fontsize=16)
    plt.title(u'广告花费与销售额对比数据', fontsize=20)
    plt.grid()#设置背景网格线的颜色,样式,尺寸和透明度
    plt.show()

    # 绘制2
    plt.figure(facecolor='w', figsize=(9, 10))
    plt.subplot(311)#三行一列的第一个
    plt.plot(data['TV'], y, 'ro')
    plt.title('TV')
    plt.grid()
    plt.subplot(312)
    plt.plot(data['Radio'], y, 'g^')
    plt.title('Radio')
    plt.grid()
    plt.subplot(313)
    plt.plot(data['Newspaper'], y, 'b*')
    plt.title('Newspaper')
    plt.grid()
    plt.tight_layout()# 紧凑显示图片
    plt.show()

    x_train, x_test, y_train, y_test = train_test_split(x, y, train_size=0.8, random_state=1)
    #train_test_split是交叉验证中常用的函数，功能是从样本中随机的按比例选取train data和testdata
    #x为所要划分的样本特征集，y所要划分的样本结果，train_size样本占比，如果是整数的话就是样本的数量，
    # random_state随机种子数，设置了种子，这样每次的随机数都是一样的
    print type(x_test)
    print x_train.shape, y_train.shape#.shape读取矩阵的长度，若设置参数，shape[0]读取第一维的长度
    linreg = LinearRegression()#线性回归
    model = linreg.fit(x_train, y_train)#训练
    print model
    print linreg.coef_, linreg.intercept_#打印参数，

    order = y_test.argsort(axis=0)
    y_test = y_test.values[order]
    x_test = x_test.values[order, :]
    y_hat = linreg.predict(x_test)
    mse = np.average((y_hat - np.array(y_test)) ** 2)  # Mean Squared Error均方差
    rmse = np.sqrt(mse)  # Root Mean Squared Error
    print 'MSE = ', mse,
    print 'RMSE = ', rmse
    print 'R2 = ', linreg.score(x_train, y_train)
    print 'R2 = ', linreg.score(x_test, y_test)

    plt.figure(facecolor='w')
    t = np.arange(len(x_test))
    plt.plot(t, y_test, 'r-', linewidth=2, label=u'真实数据')
    plt.plot(t, y_hat, 'g-', linewidth=2, label=u'预测数据')
    plt.legend(loc='upper right')
    plt.title(u'线性回归预测销量', fontsize=18)
    plt.grid(b=True)
    plt.show()

第一张图：

第二张图：

第三张图：

在这里要提一下，在训练数据时，将数据分为训练数据验证数据和测试数据。其中训练数据和验证数据是进行交叉验证的，例如：将除测试数据之外的数据分为3份，A,B,C,

当AB为训练数据时C为验证数据，AC为训练数据时B为验证数据，BC为训练数据时A为验证数据。