多项式回归将不起作用
我有一个二元多项式回归问题。
我从互联网上得到了这个示例，但似乎无法使其用于我的数据。如图所示，所作的预测令人恐惧，我无法弄清原因。我尝试了相同的代码，但提供了更多的培训数据，但这给出了更差的预测。
我假设该模型会自动显示比例。所有的自变量都很重要，所以我无法想象它需要消除。
可怜的谓词：
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
from sklearn.linear_model import LinearRegression
# Fitting Ploynomial regression to the dataset
from sklearn.preprocessing import PolynomialFeatures
#X is the independent variable (bivariate in this case)
X = np.array([[1.00000000e-01, 7.56500000e+00],
[1.00000000e-01, 8.11100000e+00],
[1.00000000e-01,8.69700000e+00],
[1.00000000e-01,9.32600000e+00],
[1.00000000e-01,1.00000000e+01],
[1.00000000e-01,1.07200000e+01],
[1.00000000e-01,1.15000000e+01],
[1.00000000e-01,1.23300000e+01],
[1.00000000e-01,1.32200000e+01],
[1.00000000e-01,1.41700000e+01],
[1.00000000e-01,1.52000000e+01],
[1.00000000e-01,1.63000000e+01],
[1.00000000e-01,1.74800000e+01],
[1.00000000e-01,1.87400000e+01],
[1.00000000e-01,2.00900000e+01],
[1.00000000e-01,2.15400000e+01],
[1.00000000e-01,2.31000000e+01],
[1.00000000e-01,2.47700000e+01],
[1.00000000e-01,2.65600000e+01],
[1.00000000e-01,2.84800000e+01],
[1.00000000e-01,3.05400000e+01],
[1.00000000e-01,3.27500000e+01],
[1.00000000e-01 , 3.51100000e+01],
[1.00000000e-01 , 3.76500000e+01],
[1.00000000e-01 , 4.03700000e+01],
[1.00000000e-01 , 4.32900000e+01],
[1.00000000e-01 , 4.64200000e+01],
[1.00000000e-01 , 4.97700000e+01],
[1.00000000e-01 , 5.33700000e+01],
[1.00000000e-01 , 5.72200000e+01],
[1.00000000e-01 , 6.13600000e+01],
[1.00000000e-01 , 6.57900000e+01],
[1.00000000e-01 , 7.05500000e+01],
[1.00000000e-01 , 7.56500000e+01],
[1.00000000e-01 , 8.11100000e+01],
[1.00000000e-01 , 8.69700000e+01],
[1.00000000e-01 , 9.32600000e+01],
[1.00000000e-01 , 1.00000000e+02],
[1.00000000e-01 , 1.07200000e+02],
[1.00000000e-01 , 1.15000000e+02],
[1.00000000e-01 , 1.23300000e+02],
[1.00000000e-01 , 1.32200000e+02],
[1.00000000e-01 , 1.41700000e+02],
[1.00000000e-01 , 1.52000000e+02],
[1.00000000e-01 , 1.63000000e+02],
[1.00000000e-01 , 1.74800000e+02],
[1.00000000e-01 , 1.87400000e+02],
[1.00000000e-01 , 2.00900000e+02],
[1.00000000e-01 , 2.15400000e+02],
[1.00000000e-01 , 2.31000000e+02],
[1.00000000e-01 , 2.47700000e+02],
[1.00000000e-01 , 2.65600000e+02],
[1.00000000e-01 , 2.84800000e+02],
[1.00000000e-01 , 3.05400000e+02],
[1.00000000e-01 , 3.27500000e+02],
[1.00000000e-01 , 3.51100000e+02],
[1.00000000e-01 , 3.76500000e+02],
[1.00000000e-01 , 4.03700000e+02],
[1.00000000e-01 , 4.32900000e+02],
[1.00000000e-01 , 4.64200000e+02],
[1.00000000e-01 , 4.97700000e+02],
[1.00000000e-01 , 5.33700000e+02],
[1.00000000e-01 , 5.72200000e+02],
[1.00000000e-01 , 6.13600000e+02],
[1.00000000e-01 , 6.57900000e+02],
[1.00000000e-01 , 7.05500000e+02],
[1.00000000e-01 , 7.56500000e+02],
[1.00000000e-01 , 8.11100000e+02],
[1.00000000e-01 , 8.69700000e+02],
[1.00000000e-01 , 9.32600000e+02],
[1.00000000e-01 , 1.00000000e+03],
[2.00000000e-01 , 7.56500000e+00],
[2.00000000e-01 , 8.11100000e+00],
[2.00000000e-01 , 8.69700000e+00],
[2.00000000e-01 , 9.32600000e+00],
[2.00000000e-01 , 1.00000000e+01],
[2.00000000e-01 , 1.07200000e+01],
[2.00000000e-01 , 1.15000000e+01],
[2.00000000e-01 , 1.23300000e+01],
[2.00000000e-01 , 1.32200000e+01],
[2.00000000e-01 , 1.41700000e+01],
[2.00000000e-01 , 1.52000000e+01],
[2.00000000e-01 , 1.63000000e+01],
[2.00000000e-01 , 1.74800000e+01],
[2.00000000e-01 , 1.87400000e+01],
[2.00000000e-01 , 2.00900000e+01],
[2.00000000e-01 , 2.15400000e+01],
[2.00000000e-01 , 2.31000000e+01],
[2.00000000e-01 , 2.47700000e+01],
[2.00000000e-01 , 2.65600000e+01],
[2.00000000e-01 , 2.84800000e+01],
[2.00000000e-01 , 3.05400000e+01],
[2.00000000e-01 , 3.27500000e+01],
[2.00000000e-01 , 3.51100000e+01],
[2.00000000e-01 , 3.76500000e+01],
[2.00000000e-01 , 4.03700000e+01],
[2.00000000e-01 , 4.32900000e+01],
[2.00000000e-01 , 4.64200000e+01],
[2.00000000e-01 , 4.97700000e+01],
[2.00000000e-01 , 5.33700000e+01],
[2.00000000e-01 , 5.72200000e+01],
[2.00000000e-01 , 6.13600000e+01],
[2.00000000e-01 , 6.57900000e+01],
[2.00000000e-01 , 7.05500000e+01],
[2.00000000e-01 , 7.56500000e+01],
[2.00000000e-01 , 8.11100000e+01],
[2.00000000e-01 , 8.69700000e+01],
[2.00000000e-01 , 9.32600000e+01],
[2.00000000e-01 , 1.00000000e+02],
[2.00000000e-01 , 1.07200000e+02],
[2.00000000e-01 , 1.15000000e+02],
[2.00000000e-01 , 1.23300000e+02],
[2.00000000e-01 , 1.32200000e+02],
[2.00000000e-01 , 1.41700000e+02],
[2.00000000e-01 , 1.52000000e+02],
[2.00000000e-01 , 1.63000000e+02],
[2.00000000e-01 , 1.74800000e+02],
[2.00000000e-01 , 1.87400000e+02],
[2.00000000e-01 , 2.00900000e+02],
[2.00000000e-01 , 2.15400000e+02],
[2.00000000e-01 , 2.31000000e+02],
[2.00000000e-01 , 2.47700000e+02],
[2.00000000e-01 , 2.65600000e+02],
[2.00000000e-01 , 2.84800000e+02],
[2.00000000e-01 , 3.05400000e+02],
[2.00000000e-01 , 3.27500000e+02],
[2.00000000e-01 , 3.51100000e+02],
[2.00000000e-01 , 3.76500000e+02],
[2.00000000e-01 , 4.03700000e+02],
[2.00000000e-01 , 4.32900000e+02],
[2.00000000e-01 , 4.64200000e+02],
[2.00000000e-01 , 4.97700000e+02],
[2.00000000e-01 , 5.33700000e+02],
[2.00000000e-01 , 5.72200000e+02],
[2.00000000e-01 , 6.13600000e+02],
[2.00000000e-01 , 6.57900000e+02],
[2.00000000e-01 , 7.05500000e+02],
[2.00000000e-01 , 7.56500000e+02],
[2.00000000e-01 , 8.11100000e+02],
[2.00000000e-01 , 8.69700000e+02],
[2.00000000e-01 , 9.32600000e+02],
[2.00000000e-01 , 1.00000000e+03],
[2.30000000e+00 , 7.56500000e+00],
[2.30000000e+00 , 8.11100000e+00],
[2.30000000e+00 , 8.69700000e+00],
[2.30000000e+00 , 9.32600000e+00],
[2.30000000e+00 , 1.00000000e+01],
[2.30000000e+00 , 1.07200000e+01],
[2.30000000e+00 , 1.15000000e+01],
[2.30000000e+00 , 1.23300000e+01],
[2.30000000e+00 , 1.32200000e+01],
[2.30000000e+00 , 1.41700000e+01],
[2.30000000e+00 , 1.52000000e+01],
[2.30000000e+00 , 1.63000000e+01],
[2.30000000e+00 , 1.74800000e+01],
[2.30000000e+00 , 1.87400000e+01],
[2.30000000e+00 , 2.00900000e+01],
[2.30000000e+00 , 2.15400000e+01],
[2.30000000e+00 , 2.31000000e+01],
[2.30000000e+00 , 2.47700000e+01],
[2.30000000e+00 , 2.65600000e+01],
[2.30000000e+00 , 2.84800000e+01],
[2.30000000e+00 , 3.05400000e+01],
[2.30000000e+00 , 3.27500000e+01],
[2.30000000e+00 , 3.51100000e+01],
[2.30000000e+00 , 3.76500000e+01],
[2.30000000e+00 , 4.03700000e+01],
[2.30000000e+00 , 4.32900000e+01],
[2.30000000e+00 , 4.64200000e+01],
[2.30000000e+00 , 4.97700000e+01],
[2.30000000e+00 , 5.33700000e+01],
[2.30000000e+00 , 5.72200000e+01],
[2.30000000e+00 , 6.13600000e+01],
[2.30000000e+00 , 6.57900000e+01],
[2.30000000e+00 , 7.05500000e+01],
[2.30000000e+00 , 7.56500000e+01],
[2.30000000e+00 , 8.11100000e+01],
[2.30000000e+00 , 8.69700000e+01],
[2.30000000e+00 , 9.32600000e+01],
[2.30000000e+00 , 1.00000000e+02],
[2.30000000e+00 , 1.07200000e+02],
[2.30000000e+00 , 1.15000000e+02],
[2.30000000e+00 , 1.23300000e+02],
[2.30000000e+00 , 1.32200000e+02],
[2.30000000e+00 , 1.41700000e+02],
[2.30000000e+00 , 1.52000000e+02],
[2.30000000e+00 , 1.63000000e+02],
[2.30000000e+00 , 1.74800000e+02],
[2.30000000e+00 , 1.87400000e+02],
[2.30000000e+00 , 2.00900000e+02],
[2.30000000e+00 , 2.15400000e+02],
[2.30000000e+00 , 2.31000000e+02],
[2.30000000e+00 , 2.47700000e+02],
[2.30000000e+00 , 2.65600000e+02],
[2.30000000e+00 , 2.84800000e+02],
[2.30000000e+00 , 3.05400000e+02],
[2.30000000e+00 , 3.27500000e+02],
[2.30000000e+00 , 3.51100000e+02],
[2.30000000e+00 , 3.76500000e+02],
[2.30000000e+00 , 4.03700000e+02],
[2.30000000e+00 , 4.32900000e+02],
[2.30000000e+00 , 4.64200000e+02],
[2.30000000e+00 , 4.97700000e+02],
[2.30000000e+00 , 5.33700000e+02],
[2.30000000e+00 , 5.72200000e+02],
[2.30000000e+00 , 6.13600000e+02],
[2.30000000e+00 , 6.57900000e+02],
[2.30000000e+00 , 7.05500000e+02],
[2.30000000e+00 , 7.56500000e+02],
[2.30000000e+00 , 8.11100000e+02],
[2.30000000e+00 , 8.69700000e+02],
[2.30000000e+00 , 9.32600000e+02],
[2.30000000e+00 , 1.00000000e+03],
[2.40000000e+00 , 7.56500000e+00],
[2.40000000e+00 , 8.11100000e+00],
[2.40000000e+00 , 8.69700000e+00],
[2.40000000e+00 , 9.32600000e+00],
[2.40000000e+00 , 1.00000000e+01],
[2.40000000e+00 , 1.07200000e+01],
[2.40000000e+00 , 1.15000000e+01],
[2.40000000e+00 , 1.23300000e+01],
[2.40000000e+00 , 1.32200000e+01],
[2.40000000e+00 , 1.41700000e+01],
[2.40000000e+00 , 1.52000000e+01],
[2.40000000e+00 , 1.63000000e+01],
[2.40000000e+00 , 1.74800000e+01],
[2.40000000e+00 , 1.87400000e+01],
[2.40000000e+00 , 2.00900000e+01],
[2.40000000e+00 , 2.15400000e+01],
[2.40000000e+00 , 2.31000000e+01],
[2.40000000e+00 , 2.47700000e+01],
[2.40000000e+00 , 2.65600000e+01],
[2.40000000e+00 , 2.84800000e+01],
[2.40000000e+00 , 3.05400000e+01],
[2.40000000e+00 , 3.27500000e+01],
[2.40000000e+00 , 3.51100000e+01],
[2.40000000e+00 , 3.76500000e+01],
[2.40000000e+00 , 4.03700000e+01],
[2.40000000e+00 , 4.32900000e+01],
[2.40000000e+00 , 4.64200000e+01],
[2.40000000e+00 , 4.97700000e+01],
[2.40000000e+00 , 5.33700000e+01],
[2.40000000e+00 , 5.72200000e+01],
[2.40000000e+00 , 6.13600000e+01],
[2.40000000e+00 , 6.57900000e+01],
[2.40000000e+00 , 7.05500000e+01],
[2.40000000e+00 , 7.56500000e+01],
[2.40000000e+00 , 8.11100000e+01],
[2.40000000e+00 , 8.69700000e+01],
[2.40000000e+00 , 9.32600000e+01],
[2.40000000e+00 , 1.00000000e+02],
[2.40000000e+00 , 1.07200000e+02],
[2.40000000e+00 , 1.15000000e+02],
[2.40000000e+00 , 1.23300000e+02],
[2.40000000e+00 , 1.32200000e+02],
[2.40000000e+00 , 1.41700000e+02],
[2.40000000e+00 , 1.52000000e+02],
[2.40000000e+00 , 1.63000000e+02],
[2.40000000e+00 , 1.74800000e+02],
[2.40000000e+00 , 1.87400000e+02],
[2.40000000e+00 , 2.00900000e+02],
[2.40000000e+00 , 2.15400000e+02],
[2.40000000e+00 , 2.31000000e+02],
[2.40000000e+00 , 2.47700000e+02],
[2.40000000e+00 , 2.65600000e+02],
[2.40000000e+00 , 2.84800000e+02],
[2.40000000e+00 , 3.05400000e+02],
[2.40000000e+00 , 3.27500000e+02],
[2.40000000e+00 , 3.51100000e+02],
[2.40000000e+00 , 3.76500000e+02],
[2.40000000e+00 , 4.03700000e+02],
[2.40000000e+00 , 4.32900000e+02],
[2.40000000e+00 , 4.64200000e+02],
[2.40000000e+00 , 4.97700000e+02],
[2.40000000e+00 , 5.33700000e+02],
[2.40000000e+00 , 5.72200000e+02],
[2.40000000e+00 , 6.13600000e+02],
[2.40000000e+00 , 6.57900000e+02],
[2.40000000e+00 , 7.05500000e+02],
[2.40000000e+00 , 7.56500000e+02],
[2.40000000e+00 , 8.11100000e+02],
[2.40000000e+00 , 8.69700000e+02],
[2.40000000e+00 , 9.32600000e+02],
[2.40000000e+00 , 1.00000000e+03]])
#X = np.loadtxt("X.txt")
#vector is the dependent data
#vector = np.loadtxt("mob_vector.txt")
vector = [ 2.12800000e+24 , 2.12100000e+24 , 2.11800000e+24 , 2.12000000e+24,
2.12400000e+24 , 2.12900000e+24 , 2.13400000e+24 , 2.14000000e+24,
2.14600000e+24 , 2.15100000e+24 , 2.15600000e+24 , 2.16100000e+24,
2.16500000e+24 , 2.16900000e+24 , 2.17300000e+24 , 2.17700000e+24,
2.18100000e+24 , 2.18600000e+24 , 2.19000000e+24 , 2.19400000e+24,
2.19900000e+24 , 2.20400000e+24 , 2.21000000e+24 , 2.21600000e+24,
2.22300000e+24 , 2.23000000e+24 , 2.23800000e+24 , 2.24700000e+24,
2.25600000e+24 , 2.26700000e+24 , 2.27800000e+24 , 2.29100000e+24,
2.30500000e+24 , 2.32000000e+24 , 2.33400000e+24 , 2.35200000e+24,
2.37000000e+24 , 2.39000000e+24 , 2.41100000e+24 , 2.43400000e+24,
2.45700000e+24 , 2.48200000e+24 , 2.50900000e+24 , 2.53600000e+24,
2.56400000e+24 , 2.59200000e+24 , 2.62000000e+24 , 2.65000000e+24,
2.68000000e+24 , 2.70600000e+24 , 2.73200000e+24 , 2.75700000e+24,
2.77900000e+24 , 2.79900000e+24 , 2.81400000e+24 , 2.82800000e+24,
2.83700000e+24 , 2.84300000e+24 , 2.84500000e+24 , 2.84300000e+24,
2.83700000e+24 , 2.82700000e+24 , 2.81400000e+24 , 2.79900000e+24,
2.78000000e+24 , 2.75800000e+24 , 2.73500000e+24 , 2.71100000e+24,
2.68600000e+24 , 2.66100000e+24 , 2.63400000e+24 , 2.11200000e+24,
2.09800000e+24 , 2.09100000e+24 , 2.08800000e+24 , 2.08900000e+24,
2.09200000e+24 , 2.09500000e+24 , 2.10000000e+24 , 2.10400000e+24,
2.10900000e+24 , 2.11300000e+24 , 2.11700000e+24 , 2.12100000e+24,
2.12400000e+24 , 2.12800000e+24 , 2.13200000e+24 , 2.13600000e+24,
2.13900000e+24 , 2.14300000e+24 , 2.14800000e+24 , 2.15200000e+24,
2.15700000e+24 , 2.16100000e+24 , 2.16700000e+24 , 2.17300000e+24,
2.18000000e+24 , 2.18800000e+24 , 2.19600000e+24 , 2.20500000e+24,
2.21400000e+24 , 2.22400000e+24 , 2.23500000e+24 , 2.24700000e+24,
2.26000000e+24 , 2.27600000e+24 , 2.29100000e+24 , 2.30800000e+24,
2.32600000e+24 , 2.34500000e+24 , 2.36600000e+24 , 2.38700000e+24,
2.40900000e+24 , 2.43200000e+24 , 2.45600000e+24 , 2.48100000e+24,
2.50700000e+24 , 2.53300000e+24 , 2.55800000e+24 , 2.58400000e+24,
2.60800000e+24 , 2.63200000e+24 , 2.65300000e+24 , 2.67300000e+24,
2.68900000e+24 , 2.70500000e+24 , 2.71500000e+24 , 2.72300000e+24,
2.72700000e+24 , 2.72700000e+24 , 2.72400000e+24 , 2.71600000e+24,
2.70600000e+24 , 2.69200000e+24 , 2.67500000e+24 , 2.65500000e+24,
2.63300000e+24 , 2.60900000e+24 , 2.58300000e+24 , 2.55700000e+24,
2.52900000e+24 , 2.50100000e+24 , 2.21400000e+24 , 2.09600000e+24,
1.98500000e+24 , 1.88800000e+24 , 1.80700000e+24 , 1.74000000e+24,
1.68800000e+24 , 1.64800000e+24 , 1.61700000e+24 , 1.59300000e+24,
1.57500000e+24 , 1.56100000e+24 , 1.55100000e+24 , 1.54200000e+24,
1.53600000e+24 , 1.53000000e+24 , 1.52600000e+24 , 1.52300000e+24,
1.52000000e+24 , 1.51700000e+24 , 1.51500000e+24 , 1.51400000e+24,
1.51300000e+24 , 1.51200000e+24 , 1.51100000e+24 , 1.51100000e+24,
1.51000000e+24 , 1.51100000e+24 , 1.51100000e+24 , 1.51200000e+24,
1.51200000e+24 , 1.51300000e+24 , 1.51400000e+24 , 1.51500000e+24,
1.51700000e+24 , 1.51800000e+24 , 1.52000000e+24 , 1.52300000e+24,
1.52500000e+24 , 1.52800000e+24 , 1.53000000e+24 , 1.53300000e+24,
1.53700000e+24 , 1.54000000e+24 , 1.54300000e+24 , 1.54600000e+24,
1.54900000e+24 , 1.55200000e+24 , 1.55500000e+24 , 1.55700000e+24,
1.55900000e+24 , 1.56000000e+24 , 1.56100000e+24 , 1.56100000e+24,
1.55900000e+24 , 1.55700000e+24 , 1.55400000e+24 , 1.55000000e+24,
1.54400000e+24 , 1.53700000e+24 , 1.52800000e+24 , 1.51800000e+24,
1.50600000e+24 , 1.49200000e+24 , 1.47700000e+24 , 1.46000000e+24,
1.44200000e+24 , 1.42300000e+24 , 1.40200000e+24 , 1.38100000e+24,
1.35800000e+24 , 2.21200000e+24 , 2.09700000e+24 , 1.98800000e+24,
1.88900000e+24 , 1.80500000e+24 , 1.73600000e+24 , 1.68000000e+24,
1.63700000e+24 , 1.60400000e+24 , 1.57900000e+24 , 1.56000000e+24,
1.54500000e+24 , 1.53400000e+24 , 1.52500000e+24 , 1.51800000e+24,
1.51200000e+24 , 1.50700000e+24 , 1.50400000e+24 , 1.50000000e+24,
1.49800000e+24 , 1.49600000e+24 , 1.49400000e+24 , 1.49300000e+24,
1.49200000e+24 , 1.49100000e+24 , 1.49000000e+24 , 1.49000000e+24,
1.49000000e+24 , 1.49000000e+24 , 1.49000000e+24 , 1.49000000e+24,
1.49100000e+24 , 1.49200000e+24 , 1.49400000e+24 , 1.49500000e+24,
1.49600000e+24 , 1.49800000e+24 , 1.49900000e+24 , 1.50200000e+24,
1.50400000e+24 , 1.50700000e+24 , 1.50900000e+24 , 1.51100000e+24,
1.51400000e+24 , 1.51700000e+24 , 1.52000000e+24 , 1.52200000e+24,
1.52500000e+24 , 1.52700000e+24 , 1.52900000e+24 , 1.53100000e+24,
1.53200000e+24 , 1.53300000e+24 , 1.53200000e+24 , 1.53100000e+24,
1.52900000e+24 , 1.52500000e+24 , 1.52100000e+24 , 1.51500000e+24,
1.50800000e+24 , 1.49900000e+24 , 1.48900000e+24 , 1.47700000e+24,
1.46400000e+24 , 1.44900000e+24 , 1.43300000e+24 , 1.41500000e+24,
1.39600000e+24 , 1.37600000e+24 , 1.35500000e+24 , 1.33300000e+24]
#e_field = np.loadtxt("e_field_vector.txt")
#e_field are the x axis values and one of the independent variables.
e_field = [ 7.565 , 8.111 , 8.697 , 9.326 , 10. , 10.72 , 11.5,
12.33 , 13.22 , 14.17 , 15.2 , 16.3 , 17.48 , 18.74,
20.09 , 21.54 , 23.1 , 24.77 , 26.56 , 28.48 , 30.54,
32.75 , 35.11 , 37.65 , 40.37 , 43.29 , 46.42 , 49.77,
53.37 , 57.22 , 61.36 , 65.79 , 70.55 , 75.65 , 81.11,
86.97 , 93.26 , 100. , 107.2 , 115. , 123.3 , 132.2,
141.7 , 152. , 163. , 174.8 , 187.4 , 200.9 , 215.4 , 231.,
247.7 , 265.6 , 284.8 , 305.4 , 327.5 , 351.1 , 376.5,
403.7 , 432.9 , 464.2 , 497.7 , 533.7 , 572.2 , 613.6,
657.9 , 705.5 , 756.5 , 811.1 , 869.7 , 932.6 , 1000. ]
for x in range(71):
#predict is an independent variable for which we'd like to predict the value
P = e_field[x]
predict= [1.6, P]
predict=np.reshape(predict,(1,-1))
#generate a model of polynomial features
poly = PolynomialFeatures(degree=2)
#transform the x data for proper fitting (for single variable type it returns,[1,x,x**2])
X_ = poly.fit_transform(X)
#transform the prediction to fit the model type
predict_ = poly.fit_transform(predict)
#here we can remove polynomial orders we don't want
#for instance I'm removing the `x` component
X_ = np.delete(X_,(1),axis=1)
predict_ = np.delete(predict_,(1),axis=1)
#generate the regression object
clf = LinearRegression()
#preform the actual regression
clf.fit(X_, vector)
#print("X_ = ",X_)
#print("predict_ = ",predict_)
#print("Prediction = ",clf.predict(predict_))
plt.scatter(X[:,1],vector, color = "red", marker = ".")
plt.scatter(e_field[x], clf.predict(predict_),color="blue", marker=".")
real_mob = [ 2.10600000e+24 , 2.02200000e+24 , 1.95500000e+24 , 1.90300000e+24,
1.86200000e+24 , 1.83200000e+24 , 1.81000000e+24 , 1.79400000e+24,
1.78200000e+24 , 1.77300000e+24 , 1.76700000e+24 , 1.76200000e+24,
1.75900000e+24 , 1.75600000e+24 , 1.75500000e+24 , 1.75400000e+24,
1.75300000e+24 , 1.75300000e+24 , 1.75300000e+24 , 1.75300000e+24,
1.75400000e+24 , 1.75500000e+24 , 1.75600000e+24 , 1.75700000e+24,
1.75800000e+24 , 1.76000000e+24 , 1.76300000e+24 , 1.76600000e+24,
1.76800000e+24 , 1.77100000e+24 , 1.77400000e+24 , 1.77800000e+24,
1.78200000e+24 , 1.78700000e+24 , 1.79300000e+24 , 1.79800000e+24,
1.80400000e+24 , 1.81000000e+24 , 1.81700000e+24 , 1.82400000e+24,
1.83200000e+24 , 1.84000000e+24 , 1.84800000e+24 , 1.85600000e+24,
1.86500000e+24 , 1.87400000e+24 , 1.88200000e+24 , 1.89100000e+24,
1.89900000e+24 , 1.90600000e+24 , 1.91300000e+24 , 1.91900000e+24,
1.92500000e+24 , 1.92900000e+24 , 1.93000000e+24 , 1.93100000e+24,
1.93000000e+24 , 1.92700000e+24 , 1.92100000e+24 , 1.91400000e+24,
1.90400000e+24 , 1.89200000e+24 , 1.87800000e+24 , 1.86200000e+24,
1.84400000e+24 , 1.82300000e+24 , 1.80100000e+24 , 1.77700000e+24,
1.75200000e+24 , 1.72600000e+24 , 1.69900000e+24]
plt.plot(e_field[0:71],real_mob,color = "green", label="Real Data")
plt.scatter(e_field[x],clf.predict(predict_) ,color="blue", label="Prediction", marker=".")
plt.scatter(X[:,1],vector,color="red", label="Training Data",marker=".")
plt.xlim(min(e_field)-1,max(e_field)+100)
#plt.yscale("log")
plt.xscale("log")
plt.title("ML prediction and real mobility data")
plt.xlabel("Reduced Electric Field (E/N)")
plt.ylabel("Mobility 1/m/V/s")
plt.legend()
3 个答案:
答案 0 :(得分：1)
当我制作X与矢量的3D散点图时，似乎没有一个简单的多项式可以很好地拟合您的帖子中的数据。请参见下图。
答案 1 :(得分：1)
正如提到的另一个答案，在每个维度中，您都有多个拐点，因此您至少需要三次回归才能匹配该属性。
您的数据也非常稀疏，除非有充分的理由说明为什么应该有一个独特的多项式来完美地模拟潜在现象，否则我会说您的预测实际上是非常好的。先验地，回归方法不知道数据在哪里以及如何填充数据中的空白。
例如，如果我告诉您f（0）= 0和f（1）= 1，您将使用哪个二次方来填补空白并找到f（0.5）？您没有足够的信息来可靠地确定这一点。数据中存在一个类似的问题，即在一个维度中，您有很多数据点，但在另一维度中，您基本上（有一个小错误）有两个带有数据的X坐标，并且您要在他们。数据太稀疏，无法可靠地做到这一点。
答案 2 :(得分：1)
得到与@James Phillips类似的数字：
\1 
您拥有2n个2D投影：
分别是：
from matplotlib import pyplot
from mpl_toolkits.mplot3d import Axes3D
fig = pyplot.figure()
ax = Axes3D(fig)
ax.scatter(X[:,0], X[:,1], vector)
我的阅读是，您有4个完美的数据组（或者可以假设它们是2个），对于每个组，您可以尝试使用高阶策略（如其他评论所讨论）。一无所获地一次对所有4个进行线性回归，因为在数据的图表2上，您的估计线平均地卡在根本没有点的组之间。基本上，您不能通过简单的线性回归有效地解决图2，而其他维度在这里无济于事。
根据数据的来源（具体是分组的性质），您可以执行以下操作：
- 通过X [：，0]手动将样本分为4组，并进行4个回归
- 如果您认为4组的点数保持相等，则另一个方向是分位数回归
- 预处理数据集，如果您觉得将来会不稳定，可以采用一些聚类过程
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