线性回归

波士顿房价预测案例

步骤

  • 导入数据
  • 数据分割
  • 数据标准化
  • 正规方程预测
  • 梯度下降预测
# 导入模块

import pandas as pd # 导入数据

from sklearn.model_selection import train_test_split # 数据分割

from sklearn.preprocessing import StandardScaler # 数据标准化

from sklearn.linear_model import LinearRegression, SGDRegressor, Ridge # 正规方程，梯度下降, 岭回归

from sklearn.metrics import mean_squared_error # 均方差

import numpy as np


# 读取Boston房价数据

boston = pd.read_csv("./boston_house_prices.csv")

y = boston["MEDV"] # MEDV为离散型目标值

x = boston.drop(["MEDV"],axis=1) # 其他数据为特征值


x
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CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX PTRATIO B LSTAT
0 0.00632 18.0 2.31 0 0.538 6.575 65.2 4.0900 1 296 15.3 396.90 4.98
1 0.02731 0.0 7.07 0 0.469 6.421 78.9 4.9671 2 242 17.8 396.90 9.14
2 0.02729 0.0 7.07 0 0.469 7.185 61.1 4.9671 2 242 17.8 392.83 4.03
3 0.03237 0.0 2.18 0 0.458 6.998 45.8 6.0622 3 222 18.7 394.63 2.94
4 0.06905 0.0 2.18 0 0.458 7.147 54.2 6.0622 3 222 18.7 396.90 5.33
... ... ... ... ... ... ... ... ... ... ... ... ... ...
501 0.06263 0.0 11.93 0 0.573 6.593 69.1 2.4786 1 273 21.0 391.99 9.67
502 0.04527 0.0 11.93 0 0.573 6.120 76.7 2.2875 1 273 21.0 396.90 9.08
503 0.06076 0.0 11.93 0 0.573 6.976 91.0 2.1675 1 273 21.0 396.90 5.64
504 0.10959 0.0 11.93 0 0.573 6.794 89.3 2.3889 1 273 21.0 393.45 6.48
505 0.04741 0.0 11.93 0 0.573 6.030 80.8 2.5050 1 273 21.0 396.90 7.88

506 rows × 13 columns

# 数据标准化需要传入二维数组，所以需要改变目标值的形状

y = np.array(y).reshape(-1, 1)


# 划分测试集和训练集

x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.25)


# 特征值标准化

std_x = StandardScaler().fit(x_train)

x_train = std_x.transform(x_train)

x_test = std_x.transform(x_test)


# 因为特征值标准化后，传入模型的系数会增大，所以目标值也需要进行标准化

std_y = StandardScaler().fit(y_train)

y_train = std_y.transform(y_train)

y_test = std_y.transform(y_test)


# 实例化线性回归

lr = LinearRegression()

# 传入测试集训练模型

lr.fit(x_train,y_train)

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LinearRegression()

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LinearRegression 
LinearRegression()
# 查看线性回归的回归系数

lr.coef_


array([[-0.11432612,  0.12922939,  0.05168773,  0.0306429 , -0.27800333,

         0.26465189,  0.02894241, -0.34962992,  0.31569604, -0.24717234,

        -0.26784233,  0.11032066, -0.41354896]])


# 线性回归预测测试集的目标值，std_y.inverse_transform：返回标准化之前的值（反标准化）

y_lr_predict = std_y.inverse_transform(lr.predict(x_test))

y_lr_predict


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# 线性回归预测的均方差（损失值）

loss_lr = mean_squared_error(std_y.inverse_transform(y_test), y_lr_predict)

loss_lr


27.89401984711536


# 实例化梯度下降回归

sgd = SGDRegressor()

sgd.fit(x_train, y_train)


D:\DeveloperTools\Anaconda\lib\site-packages\sklearn\utils\validation.py:1143: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().

  y = column_or_1d(y, warn=True)

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SGDRegressor()

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SGDRegressor 
SGDRegressor()
# 查看梯度下降回归的回归系数

sgd.coef_


array([-0.09761234,  0.08895746, -0.02421963,  0.02879482, -0.17976106,

        0.30861884, -0.00250273, -0.27224473,  0.12435245, -0.0780263 ,

       -0.24480836,  0.12012805, -0.38888841])


# 梯度下降回归预测测试集的目标值，std_y.inverse_transform：返回标准化之前的值（反标准化）

y_sgd_predict = std_y.inverse_transform(sgd.predict(x_test).reshape(-1,1))

y_sgd_predict


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# 梯度下降回归预测的均方差（损失值）

loss_sgd = mean_squared_error(std_y.inverse_transform(y_test), y_sgd_predict)

loss_sgd


28.05592202385498


# 实例化岭回归 param:alpha(正则化力度)

rd = Ridge(alpha=1.0)


# 传入训练集 训练模型

rd.fit(x_train,y_train)

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#sk-container-id-3 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before { content: "▾" }
#sk-container-id-3 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label { background-color: rgba(212, 235, 255, 1) }
#sk-container-id-3 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label { background-color: rgba(212, 235, 255, 1) }
#sk-container-id-3 input.sk-hidden--visually { border: 0; clip: rect(1px, 1px, 1px, 1px); height: 1px; margin: -1px; overflow: hidden; padding: 0; position: absolute; width: 1px }
#sk-container-id-3 div.sk-estimator { font-family: monospace; background-color: rgba(240, 248, 255, 1); border: 1px dotted rgba(0, 0, 0, 1); border-radius: 0.25em; box-sizing: border-box; margin-bottom: 0.5em }
#sk-container-id-3 div.sk-estimator:hover { background-color: rgba(212, 235, 255, 1) }
#sk-container-id-3 div.sk-parallel-item::after { content: ""; width: 100%; border-bottom: 1px solid rgba(128, 128, 128, 1); flex-grow: 1 }
#sk-container-id-3 div.sk-label:hover label.sk-toggleable__label { background-color: rgba(212, 235, 255, 1) }
#sk-container-id-3 div.sk-serial::before { content: ""; position: absolute; border-left: 1px solid rgba(128, 128, 128, 1); box-sizing: border-box; top: 0; bottom: 0; left: 50%; z-index: 0 }
#sk-container-id-3 div.sk-serial { display: flex; flex-direction: column; align-items: center; background-color: rgba(255, 255, 255, 1); padding-right: 0.2em; padding-left: 0.2em; position: relative }
#sk-container-id-3 div.sk-item { position: relative; z-index: 1 }
#sk-container-id-3 div.sk-parallel { display: flex; align-items: stretch; justify-content: center; background-color: rgba(255, 255, 255, 1); position: relative }
#sk-container-id-3 div.sk-item::before, #sk-container-id-3 div.sk-parallel-item::before { content: ""; position: absolute; border-left: 1px solid rgba(128, 128, 128, 1); box-sizing: border-box; top: 0; bottom: 0; left: 50%; z-index: -1 }
#sk-container-id-3 div.sk-parallel-item { display: flex; flex-direction: column; z-index: 1; position: relative; background-color: rgba(255, 255, 255, 1) }
#sk-container-id-3 div.sk-parallel-item:first-child::after { align-self: flex-end; width: 50% }
#sk-container-id-3 div.sk-parallel-item:last-child::after { align-self: flex-start; width: 50% }
#sk-container-id-3 div.sk-parallel-item:only-child::after { width: 0 }
#sk-container-id-3 div.sk-dashed-wrapped { border: 1px dashed rgba(128, 128, 128, 1); margin: 0 0.4em 0.5em; box-sizing: border-box; padding-bottom: 0.4em; background-color: rgba(255, 255, 255, 1) }
#sk-container-id-3 div.sk-label label { font-family: monospace; font-weight: bold; display: inline-block; line-height: 1.2em }
#sk-container-id-3 div.sk-label-container { text-align: center }
#sk-container-id-3 div.sk-container { display: inline-block !important; position: relative }
#sk-container-id-3 div.sk-text-repr-fallback { display: none } 

Ridge()

In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.

Ridge 
Ridge()
# 查看岭回归的回归系数

rd.coef_


array([[-0.11307323,  0.12670886,  0.0472335 ,  0.03097279, -0.27277927,

         0.26649452,  0.02738887, -0.34543899,  0.30352311, -0.23553989,

        -0.26624461,  0.11041044, -0.4112231 ]])


# 岭回归预测测试集的目标值，std_y.inverse_transform：返回标准化之前的值（反标准化）

y_rd_predict = std_y.inverse_transform(rd.predict(x_test))

y_rd_predict


array([[16.81586993],

       [25.62225283],

       [24.13239652],

       [23.60178301],

       [33.17482664],

       [17.47603707],

       [25.12448624],

       [14.3927178 ],

       [23.82242142],

       [33.83569284],

       [30.25910195],

       [13.28992719],

       [28.54601232],

       [34.54914571],

       [27.36491618],

       [24.87707782],

       [22.00096365],

       [14.31750595],

       [15.26655896],

       [18.95164011],

       [14.52104908],

       [37.38819398],

       [28.82792081],

       [23.3211182 ],

       [30.6343198 ],

       [20.80233876],

       [21.31839148],

       [13.79005679],

       [24.3590396 ],

       [26.87702832],

       [19.35529157],

       [32.16020072],

       [19.52355909],

       [24.26581358],

       [31.63175652],

       [30.17323569],

       [32.66670796],

       [25.47912641],

       [24.36217689],

       [24.91701584],

       [39.47302165],

       [18.22458912],

       [30.75058024],

       [32.14915944],

       [43.35075081],

       [25.58142763],

       [24.22487493],

       [22.23864659],

       [16.45656221],

       [27.14231857],

       [ 4.52270441],

       [18.23427535],

       [17.87417222],

       [14.1986027 ],

       [13.62643288],

       [34.69768313],

       [ 8.34275415],

       [23.6132958 ],

       [ 6.38923846],

       [21.27558839],

       [15.66185343],

       [29.25676316],

       [29.39607496],

       [20.06328838],

       [14.96702673],

       [20.93444425],

       [28.53639958],

       [23.76724172],

       [23.49637722],

       [11.0745397 ],

       [19.48381901],

       [15.51875938],

       [18.65960692],

       [24.24100427],

       [15.64918598],

       [14.14894164],

       [22.94337728],

       [24.09499988],

       [21.05268108],

       [28.55429725],

       [ 7.51316118],

       [22.62833775],

       [ 3.43124359],

       [15.98036192],

       [25.70480807],

       [22.57033657],

       [32.66624286],

       [17.87124766],

       [24.43818932],

       [35.27111772],

       [26.94613641],

       [17.56269425],

       [28.14078364],

       [21.18918514],

       [24.78403264],

       [-4.78164143],

       [21.36553975],

       [21.94334785],

       [16.31804996],

       [35.31337498],

       [40.90768652],

       [23.60641046],

       [19.94431495],

       [34.4813584 ],

       [21.35327276],

       [20.51324011],

       [23.90175952],

       [28.77241981],

       [40.73752328],

       [29.39270623],

       [21.38182702],

       [22.15806225],

       [31.07297608],

       [17.17452852],

       [38.05954909],

       [18.16913598],

       [25.97549364],

       [13.78567603],

       [12.51045123],

       [26.99932827],

       [18.59193795],

       [11.15468796],

       [19.52228306],

       [23.60713735],

       [18.8861402 ],

       [19.4947593 ],

       [13.61341828]])


# 岭回归预测的均方差（损失值）

loss_rd = mean_squared_error(std_y.inverse_transform(y_test), y_rd_predict)

loss_rd


27.836735080339313

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