线性回归是分析一个变量与另外一个或多个变量（自变量）之间，关系强度的方法。

线性回归的标志，如名称所暗示的那样，即自变量与结果变量之间的关系是线性的，也就是说变量关系可以连城一条直线。

模型评估：量化预测的质量

https://scikit-/stable/modules/model_evaluation.html#model-evaluation

线性回归的 7种 预测质量方法,

1、导包,

# 导包import numpy as npimport matplotlib.pyplot as plt%matplotlib inlinefrom sklearn.linear_model import LinearRegressionimport sklearn.datasets as datasets

2、加载数据集, 糖尿病数据

# 获取数据集 diabetesdata = datasets.load_diabetes()data

{'data': array([[ 0.03807591, 0.05068012, 0.06169621, ..., -0.00259226,0.01990842, -0.01764613],[-0.00188202, -0.04464164, -0.05147406, ..., -0.03949338,-0.06832974, -0.09220405],[ 0.08529891, 0.05068012, 0.04445121, ..., -0.00259226,0.00286377, -0.02593034],...,[ 0.04170844, 0.05068012, -0.01590626, ..., -0.01107952,-0.04687948, 0.01549073],[-0.04547248, -0.04464164, 0.03906215, ..., 0.02655962,0.04452837, -0.02593034],[-0.04547248, -0.04464164, -0.0730303 , ..., -0.03949338,-0.00421986, 0.00306441]]),'target': array([151., 75., 141., 206., 135., 97., 138., 63., 110., 310., 101.,69., 179., 185., 118., 171., 166., 144., 97., 168., 68., 49.,68., 245., 184., 202., 137., 85., 131., 283., 129., 59., 341.,87., 65., 102., 265., 276., 252., 90., 100., 55., 61., 92.,259., 53., 190., 142., 75., 142., 155., 225., 59., 104., 182.,128., 52., 37., 170., 170., 61., 144., 52., 128., 71., 163.,150., 97., 160., 178., 48., 270., 202., 111., 85., 42., 170.,200., 252., 113., 143., 51., 52., 210., 65., 141., 55., 134.,42., 111., 98., 164., 48., 96., 90., 162., 150., 279., 92.,83., 128., 102., 302., 198., 95., 53., 134., 144., 232., 81.,104., 59., 246., 297., 258., 229., 275., 281., 179., 200., 200.,173., 180., 84., 121., 161., 99., 109., 115., 268., 274., 158.,107., 83., 103., 272., 85., 280., 336., 281., 118., 317., 235.,60., 174., 259., 178., 128., 96., 126., 288., 88., 292., 71.,197., 186., 25., 84., 96., 195., 53., 217., 172., 131., 214.,59., 70., 220., 268., 152., 47., 74., 295., 101., 151., 127.,237., 225., 81., 151., 107., 64., 138., 185., 265., 101., 137.,143., 141., 79., 292., 178., 91., 116., 86., 122., 72., 129.,142., 90., 158., 39., 196., 222., 277., 99., 196., 202., 155.,77., 191., 70., 73., 49., 65., 263., 248., 296., 214., 185.,78., 93., 252., 150., 77., 208., 77., 108., 160., 53., 220.,154., 259., 90., 246., 124., 67., 72., 257., 262., 275., 177.,71., 47., 187., 125., 78., 51., 258., 215., 303., 243., 91.,150., 310., 153., 346., 63., 89., 50., 39., 103., 308., 116.,145., 74., 45., 115., 264., 87., 202., 127., 182., 241., 66.,94., 283., 64., 102., 200., 265., 94., 230., 181., 156., 233.,60., 219., 80., 68., 332., 248., 84., 200., 55., 85., 89.,31., 129., 83., 275., 65., 198., 236., 253., 124., 44., 172.,114., 142., 109., 180., 144., 163., 147., 97., 220., 190., 109.,191., 122., 230., 242., 248., 249., 192., 131., 237., 78., 135.,244., 199., 270., 164., 72., 96., 306., 91., 214., 95., 216.,263., 178., 113., 200., 139., 139., 88., 148., 88., 243., 71.,77., 109., 272., 60., 54., 221., 90., 311., 281., 182., 321.,58., 262., 206., 233., 242., 123., 167., 63., 197., 71., 168.,140., 217., 121., 235., 245., 40., 52., 104., 132., 88., 69.,219., 72., 201., 110., 51., 277., 63., 118., 69., 273., 258.,43., 198., 242., 232., 175., 93., 168., 275., 293., 281., 72.,140., 189., 181., 209., 136., 261., 113., 131., 174., 257., 55.,84., 42., 146., 212., 233., 91., 111., 152., 120., 67., 310.,94., 183., 66., 173., 72., 49., 64., 48., 178., 104., 132.,220., 57.]),'DESCR': '.. _diabetes_dataset:\n\nDiabetes dataset\n----------------\n\nTen baseline variables, age, sex, body mass index, average blood\npressure, and six blood serum measurements were obtained for each of n =\n442 diabetes patients, as well as the response of interest, a\nquantitative measure of disease progression one year after baseline.\n\n**Data Set Characteristics:**\n\n :Number of Instances: 442\n\n :Number of Attributes: First 10 columns are numeric predictive values\n\n :Target: Column 11 is a quantitative measure of disease progression one year after baseline\n\n :Attribute Information:\n- Age\n- Sex\n- Body mass index\n- Average blood pressure\n- S1\n- S2\n- S3\n- S4\n- S5\n- S6\n\nNote: Each of these 10 feature variables have been mean centered and scaled by the standard deviation times `n_samples` (i.e. the sum of squares of each column totals 1).\n\nSource URL:\nhttps://www4.stat.ncsu.edu/~boos/var.select/diabetes.html\n\nFor more information see:\nBradley Efron, Trevor Hastie, Iain Johnstone and Robert Tibshirani () "Least Angle Regression," Annals of Statistics (with discussion), 407-499.\n(https://web.stanford.edu/~hastie/Papers/LARS/LeastAngle_2002.pdf)','feature_names': ['age','sex','bmi','bp','s1','s2','s3','s4','s5','s6'],'data_filename': 'c:\\python37\\lib\\site-packages\\sklearn\\datasets\\data\\diabetes_data.csv.gz','target_filename': 'c:\\python37\\lib\\site-packages\\sklearn\\datasets\\data\\diabetes_target.csv.gz'}

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3、将数据分为 训练数据 和 测试数据

# 导包, 将数据分为 训练数据 和 测试数据from sklearn.model_selection import train_test_splitX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.1)display (X_train.shape, y_train.shape, X_test.shape, y_test.shape)

(397, 10)(397,)(45, 10)(45,)

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4、建模

# 使用线性回归算法 训练数据lr = LinearRegression()lr.fit(X_train, y_train)

5、预测数据

# 开始预测数据lr.predict(X_test)

array([230.00915863, 109.37448796, 135.55277842, 151.10470676,112.50492861, 60.06173076, 185.98893008, 154.37782567,226.83758259, 35.04571744, 72.66756812, 58.39584888,174.04109657, 236.22478163, 140.04573477, 179.59637478,290.40096377, 232.79655649, 127.57606558, 155.94225585,233.96170807, 122.18494431, 124.57198973, 97.73726963,261.60495587, 170.48284605, 128.85673176, 93.16011898,198.08756371, 179.37427503, 199.42069686, 106.91159532,114.42691898, 215.81999925, 200.58503886, 168.46631094,123.85604486, 118.0664, 189.81321827, 80.30230583,108.35537981, 80.98007737, 180.839016 , 83.22091387,117.70861488])

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6、查看真实数据

# 查看真实的 结果值, 与上面测试结果 对比y_test

array([246., 69., 40., 150., 107., 70., 67., 252., 236., 104., 48.,77., 311., 270., 187., 200., 270., 217., 135., 144., 280., 191.,65., 170., 303., 138., 42., 158., 222., 85., 173., 129., 68.,279., 248., 235., 111., 153., 101., 77., 72., 42., 107., 102.,183.])

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7、回归评价得分 (R²得分，决定系数)

回归评价7种方法,

https://scikit-/stable/modules/model_evaluation.html#r2-score-the-coefficient-of-determination

# 调用算法, 算出 评价分, 负无穷 到 1 的范围, 1为最好lr.score(X_test, y_test)

0.5103097598041384

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8、代码实现 预测评价(R²得分，决定系数)

'''The coefficient R^2 is defined as (1 - u/v), where u is the residualsum of squares ((y_true - y_pred) ** 2).sum() and v is the totalsum of squares ((y_true - y_true.mean()) ** 2).sum().'''

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y_pred = lr.predict(X_test).round(2)y_true = y_test# 代码实现 评价标准# 真实结果: y_true# 测试结果: y_pred

u = ((y_true - y_pred)**2).sum()

v = ((y_true - y_true.mean())**2).sum()

score = (1 - u/v)

score

0.5103097598041384

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