大数据（041）机器学习【多元线性回归实例】

一、前言

保险公司对个人投保时或根据历史数据生成的模型来计算个人保费，那么本次我们就以这个模型的求解过程为例来实践下多元线性回归。

二、数据&简单分析

我们已经获取到了一些数据（模拟数据），文件名为insurance.csv，文件内容如下。

我们可以看出数据中共有六个维度：age（年龄）,sex（性别）,bmi（肥胖指数）,children（孩子数量）,smoker（是否吸烟）,region（居住地）。charges则是当前数据人上年度在医院的花销。

所以我们可以构建一个六维高维空间来求解这个模型。

age,sex,bmi,children,smoker,region,charges
19,female,27.9,0,yes,southwest,16884.924
18,male,33.77,1,no,southeast,1725.5523
28,male,33,3,no,southeast,4449.462
33,male,22.705,0,no,northwest,21984.47061
32,male,28.88,0,no,northwest,3866.8552
31,female,25.74,0,no,southeast,3756.6216
46,female,33.44,1,no,southeast,8240.5896
37,female,27.74,3,no,northwest,7281.5056
37,male,29.83,2,no,northeast,6406.4107
60,female,25.84,0,no,northwest,28923.13692
25,male,26.22,0,no,northeast,2721.3208
62,female,26.29,0,yes,southeast,27808.7251
23,male,34.4,0,no,southwest,1826.843
56,female,39.82,0,no,southeast,11090.7178
27,male,42.13,0,yes,southeast,39611.7577
19,male,24.6,1,no,southwest,1837.237
52,female,30.78,1,no,northeast,10797.3362
23,male,23.845,0,no,northeast,2395.17155
56,male,40.3,0,no,southwest,10602.385
30,male,35.3,0,yes,southwest,36837.467
60,female,36.005,0,no,northeast,13228.84695
30,female,32.4,1,no,southwest,4149.736
18,male,34.1,0,no,southeast,1137.011
34,female,31.92,1,yes,northeast,37701.8768
37,male,28.025,2,no,northwest,6203.90175
59,female,27.72,3,no,southeast,14001.1338
63,female,23.085,0,no,northeast,14451.83515
55,female,32.775,2,no,northwest,12268.63225
23,male,17.385,1,no,northwest,2775.19215
31,male,36.3,2,yes,southwest,38711
22,male,35.6,0,yes,southwest,35585.576
18,female,26.315,0,no,northeast,2198.18985
19,female,28.6,5,no,southwest,4687.797
63,male,28.31,0,no,northwest,13770.0979
28,male,36.4,1,yes,southwest,51194.55914
19,male,20.425,0,no,northwest,1625.43375
62,female,32.965,3,no,northwest,15612.19335
26,male,20.8,0,no,southwest,2302.3
35,male,36.67,1,yes,northeast,39774.2763
60,male,39.9,0,yes,southwest,48173.361
24,female,26.6,0,no,northeast,3046.062
31,female,36.63,2,no,southeast,4949.7587
41,male,21.78,1,no,southeast,6272.4772
37,female,30.8,2,no,southeast,6313.759
38,male,37.05,1,no,northeast,6079.6715
55,male,37.3,0,no,southwest,20630.28351
18,female,38.665,2,no,northeast,3393.35635
28,female,34.77,0,no,northwest,3556.9223
60,female,24.53,0,no,southeast,12629.8967
36,male,35.2,1,yes,southeast,38709.176
18,female,35.625,0,no,northeast,2211.13075
21,female,33.63,2,no,northwest,3579.8287
48,male,28,1,yes,southwest,23568.272
36,male,34.43,0,yes,southeast,37742.5757
40,female,28.69,3,no,northwest,8059.6791
58,male,36.955,2,yes,northwest,47496.49445
58,female,31.825,2,no,northeast,13607.36875
18,male,31.68,2,yes,southeast,34303.1672
53,female,22.88,1,yes,southeast,23244.7902
34,female,37.335,2,no,northwest,5989.52365
43,male,27.36,3,no,northeast,8606.2174
25,male,33.66,4,no,southeast,4504.6624
64,male,24.7,1,no,northwest,30166.61817
28,female,25.935,1,no,northwest,4133.64165
20,female,22.42,0,yes,northwest,14711.7438
19,female,28.9,0,no,southwest,1743.214
61,female,39.1,2,no,southwest,14235.072
40,male,26.315,1,no,northwest,6389.37785
40,female,36.19,0,no,southeast,5920.1041
28,male,23.98,3,yes,southeast,17663.1442
27,female,24.75,0,yes,southeast,16577.7795
31,male,28.5,5,no,northeast,6799.458
53,female,28.1,3,no,southwest,11741.726
58,male,32.01,1,no,southeast,11946.6259
44,male,27.4,2,no,southwest,7726.854
57,male,34.01,0,no,northwest,11356.6609
29,female,29.59,1,no,southeast,3947.4131
21,male,35.53,0,no,southeast,1532.4697
22,female,39.805,0,no,northeast,2755.02095
41,female,32.965,0,no,northwest,6571.02435
31,male,26.885,1,no,northeast,4441.21315
45,female,38.285,0,no,northeast,7935.29115
22,male,37.62,1,yes,southeast,37165.1638
48,female,41.23,4,no,northwest,11033.6617
37,female,34.8,2,yes,southwest,39836.519
45,male,22.895,2,yes,northwest,21098.55405
57,female,31.16,0,yes,northwest,43578.9394
56,female,27.2,0,no,southwest,11073.176
46,female,27.74,0,no,northwest,8026.6666
55,female,26.98,0,no,northwest,11082.5772
21,female,39.49,0,no,southeast,2026.9741
53,female,24.795,1,no,northwest,10942.13205
59,male,29.83,3,yes,northeast,30184.9367
35,male,34.77,2,no,northwest,5729.0053
64,female,31.3,2,yes,southwest,47291.055
28,female,37.62,1,no,southeast,3766.8838
54,female,30.8,3,no,southwest,12105.32
55,male,38.28,0,no,southeast,10226.2842
56,male,19.95,0,yes,northeast,22412.6485
38,male,19.3,0,yes,southwest,15820.699
41,female,31.6,0,no,southwest,6186.127
30,male,25.46,0,no,northeast,3645.0894
18,female,30.115,0,no,northeast,21344.8467
61,female,29.92,3,yes,southeast,30942.1918
34,female,27.5,1,no,southwest,5003.853
20,male,28.025,1,yes,northwest,17560.37975
19,female,28.4,1,no,southwest,2331.519
26,male,30.875,2,no,northwest,3877.30425
29,male,27.94,0,no,southeast,2867.1196
63,male,35.09,0,yes,southeast,47055.5321
54,male,33.63,1,no,northwest,10825.2537
55,female,29.7,2,no,southwest,11881.358
37,male,30.8,0,no,southwest,4646.759
21,female,35.72,0,no,northwest,2404.7338
52,male,32.205,3,no,northeast,11488.31695
60,male,28.595,0,no,northeast,30259.99556
58,male,49.06,0,no,southeast,11381.3254
29,female,27.94,1,yes,southeast,19107.7796
49,female,27.17,0,no,southeast,8601.3293
37,female,23.37,2,no,northwest,6686.4313
44,male,37.1,2,no,southwest,7740.337
18,male,23.75,0,no,northeast,1705.6245
20,female,28.975,0,no,northwest,2257.47525
44,male,31.35,1,yes,northeast,39556.4945
47,female,33.915,3,no,northwest,10115.00885
26,female,28.785,0,no,northeast,3385.39915
19,female,28.3,0,yes,southwest,17081.08
52,female,37.4,0,no,southwest,9634.538
32,female,17.765,2,yes,northwest,32734.1863
38,male,34.7,2,no,southwest,6082.405
59,female,26.505,0,no,northeast,12815.44495
61,female,22.04,0,no,northeast,13616.3586
53,female,35.9,2,no,southwest,11163.568
19,male,25.555,0,no,northwest,1632.56445
20,female,28.785,0,no,northeast,2457.21115
22,female,28.05,0,no,southeast,2155.6815
19,male,34.1,0,no,southwest,1261.442
22,male,25.175,0,no,northwest,2045.68525
54,female,31.9,3,no,southeast,27322.73386
22,female,36,0,no,southwest,2166.732
34,male,22.42,2,no,northeast,27375.90478
26,male,32.49,1,no,northeast,3490.5491
34,male,25.3,2,yes,southeast,18972.495
29,male,29.735,2,no,northwest,18157.876
30,male,28.69,3,yes,northwest,20745.9891
29,female,38.83,3,no,southeast,5138.2567
46,male,30.495,3,yes,northwest,40720.55105
51,female,37.73,1,no,southeast,9877.6077
53,female,37.43,1,no,northwest,10959.6947
19,male,28.4,1,no,southwest,1842.519
35,male,24.13,1,no,northwest,5125.2157
48,male,29.7,0,no,southeast,7789.635
32,female,37.145,3,no,northeast,6334.34355
42,female,23.37,0,yes,northeast,19964.7463
40,female,25.46,1,no,northeast,7077.1894
44,male,39.52,0,no,northwest,6948.7008
48,male,24.42,0,yes,southeast,21223.6758
18,male,25.175,0,yes,northeast,15518.18025
30,male,35.53,0,yes,southeast,36950.2567
50,female,27.83,3,no,southeast,19749.38338
42,female,26.6,0,yes,northwest,21348.706
18,female,36.85,0,yes,southeast,36149.4835
54,male,39.6,1,no,southwest,10450.552
32,female,29.8,2,no,southwest,5152.134
37,male,29.64,0,no,northwest,5028.1466
47,male,28.215,4,no,northeast,10407.08585
20,female,37,5,no,southwest,4830.63
32,female,33.155,3,no,northwest,6128.79745
19,female,31.825,1,no,northwest,2719.27975
27,male,18.905,3,no,northeast,4827.90495
63,male,41.47,0,no,southeast,13405.3903
49,male,30.3,0,no,southwest,8116.68
18,male,15.96,0,no,northeast,1694.7964
35,female,34.8,1,no,southwest,5246.047
24,female,33.345,0,no,northwest,2855.43755
63,female,37.7,0,yes,southwest,48824.45
38,male,27.835,2,no,northwest,6455.86265
54,male,29.2,1,no,southwest,10436.096
46,female,28.9,2,no,southwest,8823.279
41,female,33.155,3,no,northeast,8538.28845
58,male,28.595,0,no,northwest,11735.87905
18,female,38.28,0,no,southeast,1631.8212
22,male,19.95,3,no,northeast,4005.4225
44,female,26.41,0,no,northwest,7419.4779
44,male,30.69,2,no,southeast,7731.4271
36,male,41.895,3,yes,northeast,43753.33705
26,female,29.92,2,no,southeast,3981.9768
30,female,30.9,3,no,southwest,5325.651
41,female,32.2,1,no,southwest,6775.961
29,female,32.11,2,no,northwest,4922.9159
61,male,31.57,0,no,southeast,12557.6053
36,female,26.2,0,no,southwest,4883.866
25,male,25.74,0,no,southeast,2137.6536
56,female,26.6,1,no,northwest,12044.342
18,male,34.43,0,no,southeast,1137.4697
19,male,30.59,0,no,northwest,1639.5631
39,female,32.8,0,no,southwest,5649.715
45,female,28.6,2,no,southeast,8516.829
51,female,18.05,0,no,northwest,9644.2525
64,female,39.33,0,no,northeast,14901.5167
19,female,32.11,0,no,northwest,2130.6759
48,female,32.23,1,no,southeast,8871.1517
60,female,24.035,0,no,northwest,13012.20865
27,female,36.08,0,yes,southeast,37133.8982
46,male,22.3,0,no,southwest,7147.105
28,female,28.88,1,no,northeast,4337.7352
59,male,26.4,0,no,southeast,11743.299
35,male,27.74,2,yes,northeast,20984.0936
63,female,31.8,0,no,southwest,13880.949
40,male,41.23,1,no,northeast,6610.1097
20,male,33,1,no,southwest,1980.07
40,male,30.875,4,no,northwest,8162.71625
24,male,28.5,2,no,northwest,3537.703
34,female,26.73,1,no,southeast,5002.7827
45,female,30.9,2,no,southwest,8520.026
41,female,37.1,2,no,southwest,7371.772
53,female,26.6,0,no,northwest,10355.641
27,male,23.1,0,no,southeast,2483.736
26,female,29.92,1,no,southeast,3392.9768
24,female,23.21,0,no,southeast,25081.76784
34,female,33.7,1,no,southwest,5012.471
53,female,33.25,0,no,northeast,10564.8845
32,male,30.8,3,no,southwest,5253.524
19,male,34.8,0,yes,southwest,34779.615
42,male,24.64,0,yes,southeast,19515.5416
55,male,33.88,3,no,southeast,11987.1682
28,male,38.06,0,no,southeast,2689.4954
58,female,41.91,0,no,southeast,24227.33724
41,female,31.635,1,no,northeast,7358.17565
47,male,25.46,2,no,northeast,9225.2564
42,female,36.195,1,no,northwest,7443.64305
59,female,27.83,3,no,southeast,14001.2867
19,female,17.8,0,no,southwest,1727.785
59,male,27.5,1,no,southwest,12333.828
39,male,24.51,2,no,northwest,6710.1919
40,female,22.22,2,yes,southeast,19444.2658
18,female,26.73,0,no,southeast,1615.7667
31,male,38.39,2,no,southeast,4463.2051
19,male,29.07,0,yes,northwest,17352.6803
44,male,38.06,1,no,southeast,7152.6714
23,female,36.67,2,yes,northeast,38511.6283
33,female,22.135,1,no,northeast,5354.07465
55,female,26.8,1,no,southwest,35160.13457
40,male,35.3,3,no,southwest,7196.867
63,female,27.74,0,yes,northeast,29523.1656
54,male,30.02,0,no,northwest,24476.47851
60,female,38.06,0,no,southeast,12648.7034
24,male,35.86,0,no,southeast,1986.9334
19,male,20.9,1,no,southwest,1832.094
29,male,28.975,1,no,northeast,4040.55825
18,male,17.29,2,yes,northeast,12829.4551
63,female,32.2,2,yes,southwest,47305.305
54,male,34.21,2,yes,southeast,44260.7499
27,male,30.3,3,no,southwest,4260.744
50,male,31.825,0,yes,northeast,41097.16175
55,female,25.365,3,no,northeast,13047.33235
56,male,33.63,0,yes,northwest,43921.1837
38,female,40.15,0,no,southeast,5400.9805
51,male,24.415,4,no,northwest,11520.09985
19,male,31.92,0,yes,northwest,33750.2918
58,female,25.2,0,no,southwest,11837.16
20,female,26.84,1,yes,southeast,17085.2676
52,male,24.32,3,yes,northeast,24869.8368
19,male,36.955,0,yes,northwest,36219.40545
53,female,38.06,3,no,southeast,20462.99766
46,male,42.35,3,yes,southeast,46151.1245
40,male,19.8,1,yes,southeast,17179.522
59,female,32.395,3,no,northeast,14590.63205
45,male,30.2,1,no,southwest,7441.053
49,male,25.84,1,no,northeast,9282.4806
18,male,29.37,1,no,southeast,1719.4363
50,male,34.2,2,yes,southwest,42856.838
41,male,37.05,2,no,northwest,7265.7025
50,male,27.455,1,no,northeast,9617.66245
25,male,27.55,0,no,northwest,2523.1695
47,female,26.6,2,no,northeast,9715.841
19,male,20.615,2,no,northwest,2803.69785
22,female,24.3,0,no,southwest,2150.469
59,male,31.79,2,no,southeast,12928.7911
51,female,21.56,1,no,southeast,9855.1314
40,female,28.12,1,yes,northeast,22331.5668
54,male,40.565,3,yes,northeast,48549.17835
30,male,27.645,1,no,northeast,4237.12655
55,female,32.395,1,no,northeast,11879.10405
52,female,31.2,0,no,southwest,9625.92
46,male,26.62,1,no,southeast,7742.1098
46,female,48.07,2,no,northeast,9432.9253
63,female,26.22,0,no,northwest,14256.1928
59,female,36.765,1,yes,northeast,47896.79135
52,male,26.4,3,no,southeast,25992.82104
28,female,33.4,0,no,southwest,3172.018
29,male,29.64,1,no,northeast,20277.80751
25,male,45.54,2,yes,southeast,42112.2356
22,female,28.82,0,no,southeast,2156.7518
25,male,26.8,3,no,southwest,3906.127
18,male,22.99,0,no,northeast,1704.5681
19,male,27.7,0,yes,southwest,16297.846
47,male,25.41,1,yes,southeast,21978.6769
31,male,34.39,3,yes,northwest,38746.3551
48,female,28.88,1,no,northwest,9249.4952
36,male,27.55,3,no,northeast,6746.7425
53,female,22.61,3,yes,northeast,24873.3849
56,female,37.51,2,no,southeast,12265.5069
28,female,33,2,no,southeast,4349.462
57,female,38,2,no,southwest,12646.207
29,male,33.345,2,no,northwest,19442.3535
28,female,27.5,2,no,southwest,20177.67113
30,female,33.33,1,no,southeast,4151.0287
58,male,34.865,0,no,northeast,11944.59435
41,female,33.06,2,no,northwest,7749.1564
50,male,26.6,0,no,southwest,8444.474
19,female,24.7,0,no,southwest,1737.376
43,male,35.97,3,yes,southeast,42124.5153
49,male,35.86,0,no,southeast,8124.4084
27,female,31.4,0,yes,southwest,34838.873
52,male,33.25,0,no,northeast,9722.7695
50,male,32.205,0,no,northwest,8835.26495
54,male,32.775,0,no,northeast,10435.06525
44,female,27.645,0,no,northwest,7421.19455
32,male,37.335,1,no,northeast,4667.60765
34,male,25.27,1,no,northwest,4894.7533
26,female,29.64,4,no,northeast,24671.66334
34,male,30.8,0,yes,southwest,35491.64
57,male,40.945,0,no,northeast,11566.30055
29,male,27.2,0,no,southwest,2866.091
40,male,34.105,1,no,northeast,6600.20595
27,female,23.21,1,no,southeast,3561.8889
45,male,36.48,2,yes,northwest,42760.5022
64,female,33.8,1,yes,southwest,47928.03
52,male,36.7,0,no,southwest,9144.565
61,female,36.385,1,yes,northeast,48517.56315
52,male,27.36,0,yes,northwest,24393.6224
61,female,31.16,0,no,northwest,13429.0354
56,female,28.785,0,no,northeast,11658.37915
43,female,35.72,2,no,northeast,19144.57652
64,male,34.5,0,no,southwest,13822.803
60,male,25.74,0,no,southeast,12142.5786
62,male,27.55,1,no,northwest,13937.6665
50,male,32.3,1,yes,northeast,41919.097
46,female,27.72,1,no,southeast,8232.6388
24,female,27.6,0,no,southwest,18955.22017
62,male,30.02,0,no,northwest,13352.0998
60,female,27.55,0,no,northeast,13217.0945
63,male,36.765,0,no,northeast,13981.85035
49,female,41.47,4,no,southeast,10977.2063
34,female,29.26,3,no,southeast,6184.2994
33,male,35.75,2,no,southeast,4889.9995
46,male,33.345,1,no,northeast,8334.45755
36,female,29.92,1,no,southeast,5478.0368
19,male,27.835,0,no,northwest,1635.73365
57,female,23.18,0,no,northwest,11830.6072
50,female,25.6,0,no,southwest,8932.084
30,female,27.7,0,no,southwest,3554.203
33,male,35.245,0,no,northeast,12404.8791
18,female,38.28,0,no,southeast,14133.03775
46,male,27.6,0,no,southwest,24603.04837
46,male,43.89,3,no,southeast,8944.1151
47,male,29.83,3,no,northwest,9620.3307
23,male,41.91,0,no,southeast,1837.2819
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35,male,24.42,3,yes,southeast,19361.9988
53,male,21.4,1,no,southwest,10065.413
24,female,30.1,3,no,southwest,4234.927
48,female,27.265,1,no,northeast,9447.25035
59,female,32.1,3,no,southwest,14007.222
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37,female,38.39,0,yes,southeast,40419.0191
26,male,23.7,2,no,southwest,3484.331
23,male,31.73,3,yes,northeast,36189.1017
29,male,35.5,2,yes,southwest,44585.45587
45,male,24.035,2,no,northeast,8604.48365
27,male,29.15,0,yes,southeast,18246.4955
53,male,34.105,0,yes,northeast,43254.41795
31,female,26.62,0,no,southeast,3757.8448
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50,female,30.115,1,no,northwest,9910.35985
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28,male,30.875,0,no,northwest,3062.50825
37,female,26.4,0,yes,southeast,19539.243
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64,male,37.905,0,no,northwest,14210.53595
58,female,22.77,0,no,southeast,11833.7823
24,male,33.63,4,no,northeast,17128.42608
31,male,27.645,2,no,northeast,5031.26955
39,female,22.8,3,no,northeast,7985.815
47,female,27.83,0,yes,southeast,23065.4207
30,male,37.43,3,no,northeast,5428.7277
18,male,38.17,0,yes,southeast,36307.7983
22,female,34.58,2,no,northeast,3925.7582
23,male,35.2,1,no,southwest,2416.955
33,male,27.1,1,yes,southwest,19040.876
27,male,26.03,0,no,northeast,3070.8087
45,female,25.175,2,no,northeast,9095.06825
57,female,31.825,0,no,northwest,11842.62375
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42,female,29,1,no,southwest,7050.642
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44,female,36.48,0,no,northeast,12797.20962
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51,male,33.33,3,no,southeast,10560.4917
40,male,32.3,2,no,northwest,6986.697
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35,male,34.32,3,no,southeast,5934.3798
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30,male,24.4,3,yes,southwest,18259.216
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60,male,36.955,0,no,northeast,12741.16745
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39,female,41.8,0,no,southeast,5662.225
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53,male,20.9,0,yes,southeast,21195.818
39,female,31.92,2,no,northwest,7209.4918
27,male,28.5,0,yes,northwest,18310.742
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30,female,22.895,1,no,northeast,4719.52405
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42,female,26.18,1,no,southeast,7046.7222
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21,male,22.3,1,no,southwest,2103.08
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18,male,30.14,0,no,southeast,1131.5066
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46,female,30.8,3,no,southwest,9414.92
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54,male,21.01,2,no,southeast,11013.7119
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23,male,37.1,3,no,southwest,3597.596
47,female,26.125,1,yes,northeast,23401.30575
33,female,35.53,0,yes,northwest,55135.40209
45,male,33.7,1,no,southwest,7445.918
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44,female,29.81,2,no,southeast,8219.2039
60,male,24.32,0,no,northwest,12523.6048
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56,male,31.79,2,yes,southeast,43813.8661
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41,male,30.78,3,yes,northeast,39597.4072
39,male,21.85,1,no,northwest,6117.4945
63,male,33.1,0,no,southwest,13393.756
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42,male,35.97,2,no,southeast,7160.3303
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56,female,28.31,0,no,northeast,11657.7189
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59,female,31.35,0,no,northwest,12622.1795
21,male,31.1,0,no,southwest,1526.312
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23,female,32.78,2,yes,southeast,36021.0112
57,female,29.81,0,yes,southeast,27533.9129
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60,female,32.45,0,yes,southeast,45008.9555
51,female,34.2,1,no,southwest,9872.701
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61,male,32.3,2,no,northwest,14119.62
46,female,35.53,0,yes,northeast,42111.6647
53,female,23.75,2,no,northeast,11729.6795
49,female,23.845,3,yes,northeast,24106.91255
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25,male,24.13,0,yes,northwest,15817.9857
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47,male,38.94,2,yes,southeast,44202.6536
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61,female,44,0,no,southwest,13063.883
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42,male,31.255,0,no,northwest,6358.77645
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57,male,18.335,0,no,northeast,11534.87265
51,male,42.9,2,yes,southeast,47462.894
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24,male,26.79,1,no,northwest,12609.88702
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48,male,36.67,1,no,northwest,28468.91901
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63,female,35.2,1,no,southeast,14474.675
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48,male,29.6,0,no,southwest,21232.18226
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52,female,30.875,0,no,northeast,23045.56616
25,female,33.99,1,no,southeast,3227.1211
33,female,19.095,2,yes,northeast,16776.30405
53,male,28.6,3,no,southwest,11253.421
29,male,38.94,1,no,southeast,3471.4096
58,male,36.08,0,no,southeast,11363.2832
37,male,29.8,0,no,southwest,20420.60465
54,female,31.24,0,no,southeast,10338.9316
49,female,29.925,0,no,northwest,8988.15875
50,female,26.22,2,no,northwest,10493.9458
26,male,30,1,no,southwest,2904.088
45,male,20.35,3,no,southeast,8605.3615
54,female,32.3,1,no,northeast,11512.405
38,male,38.39,3,yes,southeast,41949.2441
48,female,25.85,3,yes,southeast,24180.9335
28,female,26.315,3,no,northwest,5312.16985
23,male,24.51,0,no,northeast,2396.0959
55,male,32.67,1,no,southeast,10807.4863
41,male,29.64,5,no,northeast,9222.4026
25,male,33.33,2,yes,southeast,36124.5737
33,male,35.75,1,yes,southeast,38282.7495
30,female,19.95,3,no,northwest,5693.4305
23,female,31.4,0,yes,southwest,34166.273
46,male,38.17,2,no,southeast,8347.1643
53,female,36.86,3,yes,northwest,46661.4424
27,female,32.395,1,no,northeast,18903.49141
23,female,42.75,1,yes,northeast,40904.1995
63,female,25.08,0,no,northwest,14254.6082
55,male,29.9,0,no,southwest,10214.636
35,female,35.86,2,no,southeast,5836.5204
34,male,32.8,1,no,southwest,14358.36437
19,female,18.6,0,no,southwest,1728.897
39,female,23.87,5,no,southeast,8582.3023
27,male,45.9,2,no,southwest,3693.428
57,male,40.28,0,no,northeast,20709.02034
52,female,18.335,0,no,northwest,9991.03765
28,male,33.82,0,no,northwest,19673.33573
50,female,28.12,3,no,northwest,11085.5868
44,female,25,1,no,southwest,7623.518
26,female,22.23,0,no,northwest,3176.2877
33,male,30.25,0,no,southeast,3704.3545
19,female,32.49,0,yes,northwest,36898.73308
50,male,37.07,1,no,southeast,9048.0273
41,female,32.6,3,no,southwest,7954.517
52,female,24.86,0,no,southeast,27117.99378
39,male,32.34,2,no,southeast,6338.0756
50,male,32.3,2,no,southwest,9630.397
52,male,32.775,3,no,northwest,11289.10925
60,male,32.8,0,yes,southwest,52590.82939
20,female,31.92,0,no,northwest,2261.5688
55,male,21.5,1,no,southwest,10791.96
42,male,34.1,0,no,southwest,5979.731
18,female,30.305,0,no,northeast,2203.73595
58,female,36.48,0,no,northwest,12235.8392
43,female,32.56,3,yes,southeast,40941.2854
35,female,35.815,1,no,northwest,5630.45785
48,female,27.93,4,no,northwest,11015.1747
36,female,22.135,3,no,northeast,7228.21565
19,male,44.88,0,yes,southeast,39722.7462
23,female,23.18,2,no,northwest,14426.07385
20,female,30.59,0,no,northeast,2459.7201
32,female,41.1,0,no,southwest,3989.841
43,female,34.58,1,no,northwest,7727.2532
34,male,42.13,2,no,southeast,5124.1887
30,male,38.83,1,no,southeast,18963.17192
18,female,28.215,0,no,northeast,2200.83085
41,female,28.31,1,no,northwest,7153.5539
35,female,26.125,0,no,northeast,5227.98875
57,male,40.37,0,no,southeast,10982.5013
29,female,24.6,2,no,southwest,4529.477
32,male,35.2,2,no,southwest,4670.64
37,female,34.105,1,no,northwest,6112.35295
18,male,27.36,1,yes,northeast,17178.6824
43,female,26.7,2,yes,southwest,22478.6
56,female,41.91,0,no,southeast,11093.6229
38,male,29.26,2,no,northwest,6457.8434
29,male,32.11,2,no,northwest,4433.9159
22,female,27.1,0,no,southwest,2154.361
52,female,24.13,1,yes,northwest,23887.6627
40,female,27.4,1,no,southwest,6496.886
23,female,34.865,0,no,northeast,2899.48935
31,male,29.81,0,yes,southeast,19350.3689
42,female,41.325,1,no,northeast,7650.77375
24,female,29.925,0,no,northwest,2850.68375
25,female,30.3,0,no,southwest,2632.992
48,female,27.36,1,no,northeast,9447.3824
23,female,28.49,1,yes,southeast,18328.2381
45,male,23.56,2,no,northeast,8603.8234
20,male,35.625,3,yes,northwest,37465.34375
62,female,32.68,0,no,northwest,13844.7972
43,female,25.27,1,yes,northeast,21771.3423
23,female,28,0,no,southwest,13126.67745
31,female,32.775,2,no,northwest,5327.40025
41,female,21.755,1,no,northeast,13725.47184
58,female,32.395,1,no,northeast,13019.16105
48,female,36.575,0,no,northwest,8671.19125
31,female,21.755,0,no,northwest,4134.08245
19,female,27.93,3,no,northwest,18838.70366
19,female,30.02,0,yes,northwest,33307.5508
41,male,33.55,0,no,southeast,5699.8375
40,male,29.355,1,no,northwest,6393.60345
31,female,25.8,2,no,southwest,4934.705
37,male,24.32,2,no,northwest,6198.7518
46,male,40.375,2,no,northwest,8733.22925
22,male,32.11,0,no,northwest,2055.3249
51,male,32.3,1,no,northeast,9964.06
18,female,27.28,3,yes,southeast,18223.4512
35,male,17.86,1,no,northwest,5116.5004
59,female,34.8,2,no,southwest,36910.60803
36,male,33.4,2,yes,southwest,38415.474
37,female,25.555,1,yes,northeast,20296.86345
59,male,37.1,1,no,southwest,12347.172
36,male,30.875,1,no,northwest,5373.36425
39,male,34.1,2,no,southeast,23563.01618
18,male,21.47,0,no,northeast,1702.4553
52,female,33.3,2,no,southwest,10806.839
27,female,31.255,1,no,northwest,3956.07145
18,male,39.14,0,no,northeast,12890.05765
40,male,25.08,0,no,southeast,5415.6612
29,male,37.29,2,no,southeast,4058.1161
46,female,34.6,1,yes,southwest,41661.602
38,female,30.21,3,no,northwest,7537.1639
30,female,21.945,1,no,northeast,4718.20355
40,male,24.97,2,no,southeast,6593.5083
50,male,25.3,0,no,southeast,8442.667
20,female,24.42,0,yes,southeast,26125.67477
41,male,23.94,1,no,northeast,6858.4796
33,female,39.82,1,no,southeast,4795.6568
38,male,16.815,2,no,northeast,6640.54485
42,male,37.18,2,no,southeast,7162.0122
56,male,34.43,0,no,southeast,10594.2257
58,male,30.305,0,no,northeast,11938.25595
52,male,34.485,3,yes,northwest,60021.39897
20,female,21.8,0,yes,southwest,20167.33603
54,female,24.605,3,no,northwest,12479.70895
58,male,23.3,0,no,southwest,11345.519
45,female,27.83,2,no,southeast,8515.7587
26,male,31.065,0,no,northwest,2699.56835
63,female,21.66,0,no,northeast,14449.8544
58,female,28.215,0,no,northwest,12224.35085
37,male,22.705,3,no,northeast,6985.50695
25,female,42.13,1,no,southeast,3238.4357
52,male,41.8,2,yes,southeast,47269.854
64,male,36.96,2,yes,southeast,49577.6624
22,female,21.28,3,no,northwest,4296.2712
28,female,33.11,0,no,southeast,3171.6149
18,male,33.33,0,no,southeast,1135.9407
28,male,24.3,5,no,southwest,5615.369
45,female,25.7,3,no,southwest,9101.798
33,male,29.4,4,no,southwest,6059.173
18,female,39.82,0,no,southeast,1633.9618
32,male,33.63,1,yes,northeast,37607.5277
24,male,29.83,0,yes,northeast,18648.4217
19,male,19.8,0,no,southwest,1241.565
20,male,27.3,0,yes,southwest,16232.847
40,female,29.3,4,no,southwest,15828.82173
34,female,27.72,0,no,southeast,4415.1588
42,female,37.9,0,no,southwest,6474.013
51,female,36.385,3,no,northwest,11436.73815
54,female,27.645,1,no,northwest,11305.93455
55,male,37.715,3,no,northwest,30063.58055
52,female,23.18,0,no,northeast,10197.7722
32,female,20.52,0,no,northeast,4544.2348
28,male,37.1,1,no,southwest,3277.161
41,female,28.05,1,no,southeast,6770.1925
43,female,29.9,1,no,southwest,7337.748
49,female,33.345,2,no,northeast,10370.91255
64,male,23.76,0,yes,southeast,26926.5144
55,female,30.5,0,no,southwest,10704.47
24,male,31.065,0,yes,northeast,34254.05335
20,female,33.3,0,no,southwest,1880.487
45,male,27.5,3,no,southwest,8615.3
26,male,33.915,1,no,northwest,3292.52985
25,female,34.485,0,no,northwest,3021.80915
43,male,25.52,5,no,southeast,14478.33015
35,male,27.61,1,no,southeast,4747.0529
26,male,27.06,0,yes,southeast,17043.3414
57,male,23.7,0,no,southwest,10959.33
22,female,30.4,0,no,northeast,2741.948
32,female,29.735,0,no,northwest,4357.04365
39,male,29.925,1,yes,northeast,22462.04375
25,female,26.79,2,no,northwest,4189.1131
48,female,33.33,0,no,southeast,8283.6807
47,female,27.645,2,yes,northwest,24535.69855
18,female,21.66,0,yes,northeast,14283.4594
18,male,30.03,1,no,southeast,1720.3537
61,male,36.3,1,yes,southwest,47403.88
47,female,24.32,0,no,northeast,8534.6718
28,female,17.29,0,no,northeast,3732.6251
36,female,25.9,1,no,southwest,5472.449
20,male,39.4,2,yes,southwest,38344.566
44,male,34.32,1,no,southeast,7147.4728
38,female,19.95,2,no,northeast,7133.9025
19,male,34.9,0,yes,southwest,34828.654
21,male,23.21,0,no,southeast,1515.3449
46,male,25.745,3,no,northwest,9301.89355
58,male,25.175,0,no,northeast,11931.12525
20,male,22,1,no,southwest,1964.78
18,male,26.125,0,no,northeast,1708.92575
28,female,26.51,2,no,southeast,4340.4409
33,male,27.455,2,no,northwest,5261.46945
19,female,25.745,1,no,northwest,2710.82855
45,male,30.36,0,yes,southeast,62592.87309
62,male,30.875,3,yes,northwest,46718.16325
25,female,20.8,1,no,southwest,3208.787
43,male,27.8,0,yes,southwest,37829.7242
42,male,24.605,2,yes,northeast,21259.37795
24,female,27.72,0,no,southeast,2464.6188
29,female,21.85,0,yes,northeast,16115.3045
32,male,28.12,4,yes,northwest,21472.4788
25,female,30.2,0,yes,southwest,33900.653
41,male,32.2,2,no,southwest,6875.961
42,male,26.315,1,no,northwest,6940.90985
33,female,26.695,0,no,northwest,4571.41305
34,male,42.9,1,no,southwest,4536.259
19,female,34.7,2,yes,southwest,36397.576
30,female,23.655,3,yes,northwest,18765.87545
18,male,28.31,1,no,northeast,11272.33139
19,female,20.6,0,no,southwest,1731.677
18,male,53.13,0,no,southeast,1163.4627
35,male,39.71,4,no,northeast,19496.71917
39,female,26.315,2,no,northwest,7201.70085
31,male,31.065,3,no,northwest,5425.02335
62,male,26.695,0,yes,northeast,28101.33305
62,male,38.83,0,no,southeast,12981.3457
42,female,40.37,2,yes,southeast,43896.3763
31,male,25.935,1,no,northwest,4239.89265
61,male,33.535,0,no,northeast,13143.33665
42,female,32.87,0,no,northeast,7050.0213
51,male,30.03,1,no,southeast,9377.9047
23,female,24.225,2,no,northeast,22395.74424
52,male,38.6,2,no,southwest,10325.206
57,female,25.74,2,no,southeast,12629.1656
23,female,33.4,0,no,southwest,10795.93733
52,female,44.7,3,no,southwest,11411.685
50,male,30.97,3,no,northwest,10600.5483
18,female,31.92,0,no,northeast,2205.9808
18,female,36.85,0,no,southeast,1629.8335
21,female,25.8,0,no,southwest,2007.945
61,female,29.07,0,yes,northwest,29141.3603

三、模型构建

我们定义六个维度X1到X6，分别代表age到region。其中给Xn设置一个βn作为模型变量。定义Y表示charges。

四、使用R语言求解模型

我们先准备好insurance.csv数据文件放入RStudio工作空间中。打开RStudio。

编辑代码如下：

insurance <- read.csv("insurance.csv", stringsAsFactors = TRUE)
str(insurance)#既然因变量是charges,我们就来看一下它是如何分布的
summary(insurance$charges)
hist(insurance$charges)table(insurance$region)
cor(insurance[c("age","bmi","children","charges")])
pairs(insurance[c("age","bmi","children","charges")])library("psych")
pairs.panels(insurance[c("age","bmi","children","charges")])ins_model <- lm(charges ~ age + children + bmi + sex + smoker + region, data=insurance)
ins_model <- lm(charges ~ . , data=insurance)
ins_model
summary(ins_model)insurance$age2 <- insurance$age^2
insurance$bmi30 <- ifelse(insurance$bmi >= 30, 1, 0)ins_models <- lm(charges ~ age + age2 + children + bmi + sex + bmi30*smoker + region , data=insurance)
summary(ins_models)

五、代码分析

1、读取文件

执行下方代码，读取历史数据文件。

insurance <- read.csv("insurance.csv", stringsAsFactors = TRUE)

结果如下图，我们已经将insurance.csv内容读取到了变量insurance中。

2、转换数据类型

执行下方命令将insurance中数据转换为因子类型。

str(insurance)

执行后结果如下

3、分析报销情况

执行下方命令分析报销情况

summary(insurance$charges)

执行后结果如下图

其中红框所示为执行结果，其由左至右依次显示最小值数、1/4位数、中位数、平均值、3/4位数、最大数。

4、查看柱状图

执行下方命令查看柱状图

hist(insurance$charges)

执行后结果如下图

我们可以看到红框所示为对报销情况统计的柱状图。

5、查看地区分布

执行下方命令，查看地区分布情况

table(insurance$region)

执行结果如下图

我们可以看出，东北、戏本、东南、西南人数样本分布还是比较均匀的。

6、求相关系数

执行下方命令，查看维度之间相关系数

cor(insurance[c("age","bmi","children","charges")])

执行结果如下图

从图示表中可以看到年龄、肥胖系数、孩子数量、报销费用之间的相关系数

7、获取散点矩阵图

执行下方命令，查看维度之间的散点矩阵图

pairs(insurance[c("age","bmi","children","charges")])

执行结果如下图

8、引入第三方软件包，求解相关系数及其散点矩阵图

执行下方操作

8.1、如下图引入第三方软件包

8.2、执行下方命令

library("psych")
pairs.panels(insurance[c("age","bmi","children","charges")])

简单分析一下图中数据，

以左上到右下为中轴线，上半部分为各个维度之间的相关系数。相关系数越趋近于1代表越正相关，越趋近于-1代表越负相关，越趋近于0代表不相关。因此我们可以利用相关系数进行降维，将一些不相关的维度剔除。

由上图可以看出年龄、肥胖指数与保费成正相关，分别为0.3和0.2。这也符合我们的预期，年龄越大、肥胖指数越高，医院花销就越高。

8.3、执行下方命令

ins_model <- lm(charges ~ age + children + bmi + sex + smoker + region, data=insurance)

或

ins_model <- lm(charges ~ . , data=insurance)
得到下图所示结果，其中coefficients就是系数。这样看起来不太直观，我们可以按照8.3步将ins_model打印出来。

8.4、打印ins_model

ins_model

下图中就很明显的显示了各个维度的系数。其中age=256.9表示年龄每增长1岁，每年就要多支出256.9的医疗费；sexmale=-131.3表示male要比female少交131.3的医疗费；bmi=339.2表示肥胖指数每增加一个点就要多交339.2的医疗费；children475.5表示孩子数量每增加一个每年就多支出475.5的医疗费；smokeryes=23848.5表示抽烟的要比不抽烟的多支出23848.5的医疗费；regionnorthwest、regionsoutheast、regionsouthwest是与southwest比较而言的，与sexmale类似。

那么问题来了，为什么sex、smoker和region被区分开了，其余维度没有被区分开。其实因为之前我们定义数据时将sex、smoker和region定义成了因子类型，其余都是数值类型。

8.5、打印模型统计摘要

summary(ins_model)

8.6、模型优化

为了使数据更好的回归线性，我们可以在模型数据中新增两个列，其中age2值为age的平方，bmi30代表肥胖指数是否大于30（大于30才算真正的肥胖，低于30成为不肥胖）

insurance$age2 <- insurance$age^2

insurance$bmi30 <- ifelse(insurance$bmi >= 30, 1, 0)

8.7、运算模型

ins_models <- lm(charges ~ age + age2 + children + bmi + sex + bmi30*smoker + region , data=insurance)

这里引入了我们的age2和bim30，这称之为升维度。但是为什么要用bmi30*smoker呢，因为在很了解数据的前提下，我们知道肥胖且抽烟会导致医疗费用支出增大，单一的一项并没有很明显的影响。因此就使用了bmi30*smoker。

8.8、打印优化后模型统计摘要

summary(ins_models)

从下图可以看出升维的age2和bmi30相关性很大，这也证实了本次模型优化是成功的。

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