機器學習之線性迴歸預測銷量

背景：給出廣告在TV,Radio,Newspaper的銷售額，利用線性迴歸預測其以後的銷量趨勢

數據：

	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'
    # # 手寫讀取數據
    # 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自帶庫
    # f = file(path, 'r')
    # print f
    # d = csv.reader(f)
    # for line in d:
    #     print line
    # f.close()

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

    # pandas讀入
    data = pd.read_csv(path)    # TV、Radio、Newspaper、Sales讀取數據
    x = data[['TV', 'Radio', 'Newspaper']]
    # x = data[['TV', 'Radio']]
    y = data['Sales']
    print x
    print y

    mpl.rcParams['font.sans-serif'] = [u'simHei']#指定默認字體
    mpl.rcParams['axes.unicode_minus'] = False#解決保存圖像是負號'-'顯示爲方塊的問題

    # 繪製1，主要目的：看着三組數據的分佈情況
    plt.figure(facecolor='w')#畫布顏色爲白色
    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')#圖例在右下方
    plt.xlabel(u'廣告花費', fontsize=16)
    plt.ylabel(u'銷售額', fontsize=16)
    plt.title(u'廣告花費與銷售額對比數據', fontsize=20)
    plt.grid()#設置背景網格線的顏色,樣式,尺寸和透明度
    plt.show()

    # 繪製2
    plt.figure(facecolor='w', figsize=(9, 10))
    plt.subplot(311)#三行一列的第一個
    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()# 緊湊顯示圖片
    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是交叉驗證中常用的函數，功能是從樣本中隨機的按比例選取train data和testdata
    #x爲所要劃分的樣本特徵集，y所要劃分的樣本結果，train_size樣本佔比，如果是整數的話就是樣本的數量，
    # random_state隨機種子數，設置了種子，這樣每次的隨機數都是一樣的
    print type(x_test)
    print x_train.shape, y_train.shape#.shape讀取矩陣的長度，若設置參數，shape[0]讀取第一維的長度
    linreg = LinearRegression()#線性迴歸
    model = linreg.fit(x_train, y_train)#訓練
    print model
    print linreg.coef_, linreg.intercept_#打印參數，

    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'真實數據')
    plt.plot(t, y_hat, 'g-', linewidth=2, label=u'預測數據')
    plt.legend(loc='upper right')
    plt.title(u'線性迴歸預測銷量', fontsize=18)
    plt.grid(b=True)
    plt.show()

第一張圖：

第二張圖：

第三張圖：

在這裏要提一下，在訓練數據時，將數據分爲訓練數據驗證數據和測試數據。其中訓練數據和驗證數據是進行交叉驗證的，例如：將除測試數據之外的數據分爲3份，A,B,C,

當AB爲訓練數據時C爲驗證數據，AC爲訓練數據時B爲驗證數據，BC爲訓練數據時A爲驗證數據。