Linear regression is variable between a further one or more variables (independent variables), the relationship between the intensity of the analysis method.
Linear regression of the signs, as the name implies, namely the relationship between the independent variables and the outcome variables is linear, that is to say the relationship between variables can Citylink a straight line.
Model assessment: quantitative forecast quality
https://scikit-learn.org/stable/modules/model_evaluation.html#model-evaluation
7 kinds of quality prediction method for linear regression,
1, the leader packet,
# 导包 import numpy as np import matplotlib.pyplot as plt %matplotlib inline from sklearn.linear_model import LinearRegression import sklearn.datasets as datasets
2, the data set is loaded, diabetes data
# Get the data set Diabetes Data = 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 (2004) "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'}
3, the data is divided into training data and test data
# Leader packet, the data into training and testing data from sklearn.model_selection Import train_test_split X_train, X_test, y_train, android.permission.FACTOR. = Train_test_split (X-, Y, test_size = 0.1 ) the display (X_train.shape, y_train.shape, X_test.shape , y_test.shape)
(397, 10) (397,) (45, 10) (45,)
4, modeling
# Using linear regression algorithm training data LR = LinearRegression () lr.fit (X_train, y_train)
5, forecast data
# Start predicting data 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, 118.02004664, 189.81321827, 80.30230583, 108.35537981, 80.98007737, 180.839016 , 83.22091387, 117.70861488])
6, to see real data
# View the true value of the results, compared with the above test results 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.])
7, return the evaluation score (R² score, coefficient of determination)
Regression Analysis 7 Ways,
# Call the algorithm calculates the evaluation points, minus infinity to 1 range, 1 is the best lr.score (X_test, y_test)
0.5103097598041384
8, code implements predictive evaluation (R ² score, coefficient of determination)
''' The coefficient R^2 is defined as (1 - u/v), where u is the residual sum of squares ((y_true - y_pred) ** 2).sum() and v is the total sum of squares ((y_true - y_true.mean()) ** 2).sum(). '''
= lr.predict y_pred (X_test) .round (2 ) y_true = android.permission.FACTOR. # code for evaluation standard # actual results: y_true # Test Results: y_pred
u = ((y_true - y_pred)**2).sum()
v = ((y_true - y_true.mean())**2).sum()
score = (1 - u/v)
score
0.5103097598041384