Linear Regression Returns Different Results Than Synthetic Parameters

trying this code: from sklearn import linear_model import numpy as np x1 = np.arange(0,10,0.1) x2 = x1*10 y = 2*x1 + 3*x2 X = np.vstack((x1, x2)).transpose() reg_model = linear_

Solution 1:

Your problem is with the uniqueness of solutions, as both dimensions are the same (applying a linear transform to one dimension does not make unique data in the eyes of this model), you get an infinite number of possible solutions that will fit you data. Applying a non-linear transformation to your second dimension you will see the desired output.

from sklearn import linear_model
import numpy as np

x1 = np.arange(0,10,0.1)
x2 = x1**2
X = np.vstack((x1, x2)).transpose()
y = 2*x1 + 3*x2

reg_model = linear_model.LinearRegression()
reg_model.fit(X,y)
print reg_model.coef_
# should be [2,3]print reg_model.predict([[5,6]])
# should be 2*5 + 3*6 = 28 print reg_model.intercept_
# perfectly at the expected value of 0print reg_model.score(X,y)

Outputs are

• [ 2. 3.]
• [ 28.]
• -2.84217094304e-14
• 1.0