机器学习实战——Topic1使用线性回归构建房价预测模型

一、题设

        线性回归是最简单和经典的回归模型。 假设输入xx为dd维，预测目标yy为连续型取值。线性回归的模型形式为：y=w0+w1x1+…+wdxdy=w0+w1x1+…+wdxd

        下面我们通过线性回归构建房价预测模型，回归系数使用最小二乘法来估计。 我们的案例基于波士顿房价数据集，使用sklearn.linear_model模块提供的线性回归函数，构建房价预测模型，预测房价。

        1.样本数：506

        2.特征数量：13个连续特征（包括“类”属性“MEDV”），1个二进制值特征。

特征	说明
CRIM	城镇人均犯罪率
ZN	大于25,000平方英尺的地块划分为住宅用地的比例
INDUS	每个城镇非零售业务的比例
CHAS	查尔斯河虚拟变量（如果管道界限= 1则为河; =0则不为河）
NOX	一氧化氮浓度（每千万份）
RM	每间住宅的平均房间数
AGE	自住房屋是在1940年之前建造的比例
DIS	到加州五个就业中心的加权距离
RAD	对径向高速公路的可达性指数
TAX	每10,000美元的全价物业税
PTRATIO	城镇的学生与教师比例
B	1000（Bk-0.63）^ 2其中Bk是城镇的黑人的比例
LSTAT	低社会阶层人口比例％
MEDV	以1000美元为单位的自住房屋的中位数价值

        sklearn.linear_model模块包含了常见的线性模型，即“预测目标能够表示成输入变量的线性组合形式”的模型。

        在我们的例子中 y = 波士顿房价。x = 其余的输入变量。 首先，我们导入sklearn的linear_model模块。 然后将预测变量从DataFrame中删除。 最后创建一个线性模型对象mode。

二、DATASET

bd网盘链接: https://pan.baidu.com/s/1YQvi5hf8iJ3CPtvSAZYQWg

提取码: 8888 

Boston_housing_data.csv

CRIM,ZN,INDUS,CHAS,NOX,RM,AGE,DIS,RAD,TAX,PIRATIO,B,LSTAT,TARGET
0.00632,18,2.31,0,0.538,6.575,65.2,4.09,1,296,15.3,396.9,4.98,24
0.02731,0,7.07,0,0.469,6.421,78.9,4.9671,2,242,17.8,396.9,9.14,21.6
0.02729,0,7.07,0,0.469,7.185,61.1,4.9671,2,242,17.8,392.83,4.03,34.7
0.03237,0,2.18,0,0.458,6.998,45.8,6.0622,3,222,18.7,394.63,2.94,33.4
0.06905,0,2.18,0,0.458,7.147,54.2,6.0622,3,222,18.7,396.9,5.33,36.2
0.02985,0,2.18,0,0.458,6.43,58.7,6.0622,3,222,18.7,394.12,5.21,28.7
0.08829,12.5,7.87,0,0.524,6.012,66.6,5.5605,5,311,15.2,395.6,12.43,22.9
0.14455,12.5,7.87,0,0.524,6.172,96.1,5.9505,5,311,15.2,396.9,19.15,27.1
0.21124,12.5,7.87,0,0.524,5.631,100,6.0821,5,311,15.2,386.63,29.93,16.5
0.17004,12.5,7.87,0,0.524,6.004,85.9,6.5921,5,311,15.2,386.71,17.1,18.9
0.22489,12.5,7.87,0,0.524,6.377,94.3,6.3467,5,311,15.2,392.52,20.45,15
0.11747,12.5,7.87,0,0.524,6.009,82.9,6.2267,5,311,15.2,396.9,13.27,18.9
0.09378,12.5,7.87,0,0.524,5.889,39,5.4509,5,311,15.2,390.5,15.71,21.7
0.62976,0,8.14,0,0.538,5.949,61.8,4.7075,4,307,21,396.9,8.26,20.4
0.63796,0,8.14,0,0.538,6.096,84.5,4.4619,4,307,21,380.02,10.26,18.2
0.62739,0,8.14,0,0.538,5.834,56.5,4.4986,4,307,21,395.62,8.47,19.9
1.05393,0,8.14,0,0.538,5.935,29.3,4.4986,4,307,21,386.85,6.58,23.1
0.7842,0,8.14,0,0.538,5.99,81.7,4.2579,4,307,21,386.75,14.67,17.5
0.80271,0,8.14,0,0.538,5.456,36.6,3.7965,4,307,21,288.99,11.69,20.2
0.7258,0,8.14,0,0.538,5.727,69.5,3.7965,4,307,21,390.95,11.28,18.2
1.25179,0,8.14,0,0.538,5.57,98.1,3.7979,4,307,21,376.57,21.02,13.6
0.85204,0,8.14,0,0.538,5.965,89.2,4.0123,4,307,21,392.53,13.83,19.6
1.23247,0,8.14,0,0.538,6.142,91.7,3.9769,4,307,21,396.9,18.72,15.2
0.98843,0,8.14,0,0.538,5.813,100,4.0952,4,307,21,394.54,19.88,14.5
0.75026,0,8.14,0,0.538,5.924,94.1,4.3996,4,307,21,394.33,16.3,15.6
0.84054,0,8.14,0,0.538,5.599,85.7,4.4546,4,307,21,303.42,16.51,13.9
0.67191,0,8.14,0,0.538,5.813,90.3,4.682,4,307,21,376.88,14.81,16.6
0.95577,0,8.14,0,0.538,6.047,88.8,4.4534,4,307,21,306.38,17.28,14.8
0.77299,0,8.14,0,0.538,6.495,94.4,4.4547,4,307,21,387.94,12.8,18.4
1.00245,0,8.14,0,0.538,6.674,87.3,4.239,4,307,21,380.23,11.98,21
1.13081,0,8.14,0,0.538,5.713,94.1,4.233,4,307,21,360.17,22.6,12.7
1.35472,0,8.14,0,0.538,6.072,100,4.175,4,307,21,376.73,13.04,14.5
1.38799,0,8.14,0,0.538,5.95,82,3.99,4,307,21,232.6,27.71,13.2
1.15172,0,8.14,0,0.538,5.701,95,3.7872,4,307,21,358.77,18.35,13.1
1.61282,0,8.14,0,0.538,6.096,96.9,3.7598,4,307,21,248.31,20.34,13.5
0.06417,0,5.96,0,0.499,5.933,68.2,3.3603,5,279,19.2,396.9,9.68,18.9
0.09744,0,5.96,0,0.499,5.841,61.4,3.3779,5,279,19.2,377.56,11.41,20
0.08014,0,5.96,0,0.499,5.85,41.5,3.9342,5,279,19.2,396.9,8.77,21
0.17505,0,5.96,0,0.499,5.966,30.2,3.8473,5,279,19.2,393.43,10.13,24.7
0.02763,75,2.95,0,0.428,6.595,21.8,5.4011,3,252,18.3,395.63,4.32,30.8
0.03359,75,2.95,0,0.428,7.024,15.8,5.4011,3,252,18.3,395.62,1.98,34.9
0.12744,0,6.91,0,0.448,6.77,2.9,5.7209,3,233,17.9,385.41,4.84,26.6
0.1415,0,6.91,0,0.448,6.169,6.6,5.7209,3,233,17.9,383.37,5.81,25.3
0.15936,0,6.91,0,0.448,6.211,6.5,5.7209,3,233,17.9,394.46,7.44,24.7
0.12269,0,6.91,0,0.448,6.069,40,5.7209,3,233,17.9,389.39,9.55,21.2
0.17142,0,6.91,0,0.448,5.682,33.8,5.1004,3,233,17.9,396.9,10.21,19.3
0.18836,0,6.91,0,0.448,5.786,33.3,5.1004,3,233,17.9,396.9,14.15,20
0.22927,0,6.91,0,0.448,6.03,85.5,5.6894,3,233,17.9,392.74,18.8,16.6
0.25387,0,6.91,0,0.448,5.399,95.3,5.87,3,233,17.9,396.9,30.81,14.4
0.21977,0,6.91,0,0.448,5.602,62,6.0877,3,233,17.9,396.9,16.2,19.4
0.08873,21,5.64,0,0.439,5.963,45.7,6.8147,4,243,16.8,395.56,13.45,19.7
0.04337,21,5.64,0,0.439,6.115,63,6.8147,4,243,16.8,393.97,9.43,20.5
0.0536,21,5.64,0,0.439,6.511,21.1,6.8147,4,243,16.8,396.9,5.28,25
0.04981,21,5.64,0,0.439,5.998,21.4,6.8147,4,243,16.8,396.9,8.43,23.4
0.0136,75,4,0,0.41,5.888,47.6,7.3197,3,469,21.1,396.9,14.8,18.9
0.01311,90,1.22,0,0.403,7.249,21.9,8.6966,5,226,17.9,395.93,4.81,35.4
0.02055,85,0.74,0,0.41,6.383,35.7,9.1876,2,313,17.3,396.9,5.77,24.7
0.01432,100,1.32,0,0.411,6.816,40.5,8.3248,5,256,15.1,392.9,3.95,31.6
0.15445,25,5.13,0,0.453,6.145,29.2,7.8148,8,284,19.7,390.68,6.86,23.3
0.10328,25,5.13,0,0.453,5.927,47.2,6.932,8,284,19.7,396.9,9.22,19.6
0.14932,25,5.13,0,0.453,5.741,66.2,7.2254,8,284,19.7,395.11,13.15,18.7
0.17171,25,5.13,0,0.453,5.966,93.4,6.8185,8,284,19.7,378.08,14.44,16
0.11027,25,5.13,0,0.453,6.456,67.8,7.2255,8,284,19.7,396.9,6.73,22.2
0.1265,25,5.13,0,0.453,6.762,43.4,7.9809,8,284,19.7,395.58,9.5,25
0.01951,17.5,1.38,0,0.4161,7.104,59.5,9.2229,3,216,18.6,393.24,8.05,33
0.03584,80,3.37,0,0.398,6.29,17.8,6.6115,4,337,16.1,396.9,4.67,23.5
0.04379,80,3.37,0,0.398,5.787,31.1,6.6115,4,337,16.1,396.9,10.24,19.4
0.05789,12.5,6.07,0,0.409,5.878,21.4,6.498,4,345,18.9,396.21,8.1,22
0.13554,12.5,6.07,0,0.409,5.594,36.8,6.498,4,345,18.9,396.9,13.09,17.4
0.12816,12.5,6.07,0,0.409,5.885,33,6.498,4,345,18.9,396.9,8.79,20.9
0.08826,0,10.81,0,0.413,6.417,6.6,5.2873,4,305,19.2,383.73,6.72,24.2
0.15876,0,10.81,0,0.413,5.961,17.5,5.2873,4,305,19.2,376.94,9.88,21.7
0.09164,0,10.81,0,0.413,6.065,7.8,5.2873,4,305,19.2,390.91,5.52,22.8
0.19539,0,10.81,0,0.413,6.245,6.2,5.2873,4,305,19.2,377.17,7.54,23.4
0.07896,0,12.83,0,0.437,6.273,6,4.2515,5,398,18.7,394.92,6.78,24.1
0.09512,0,12.83,0,0.437,6.286,45,4.5026,5,398,18.7,383.23,8.94,21.4
0.10153,0,12.83,0,0.437,6.279,74.5,4.0522,5,398,18.7,373.66,11.97,20
0.08707,0,12.83,0,0.437,6.14,45.8,4.0905,5,398,18.7,386.96,10.27,20.8
0.05646,0,12.83,0,0.437,6.232,53.7,5.0141,5,398,18.7,386.4,12.34,21.2
0.08387,0,12.83,0,0.437,5.874,36.6,4.5026,5,398,18.7,396.06,9.1,20.3
0.04113,25,4.86,0,0.426,6.727,33.5,5.4007,4,281,19,396.9,5.29,28
0.04462,25,4.86,0,0.426,6.619,70.4,5.4007,4,281,19,395.63,7.22,23.9
0.03659,25,4.86,0,0.426,6.302,32.2,5.4007,4,281,19,396.9,6.72,24.8
0.03551,25,4.86,0,0.426,6.167,46.7,5.4007,4,281,19,390.64,7.51,22.9
0.05059,0,4.49,0,0.449,6.389,48,4.7794,3,247,18.5,396.9,9.62,23.9
0.05735,0,4.