How to make a polynomial regression with sklearn

Question

I have some data that doesn't fit a linear regression:

In fact should fit a quadratic function 'exactly':

P = R*I**2 

I'm making this:

model = sklearn.linear_model.LinearRegression()

X = alambres[alambre]['mediciones'][x].reshape(-1, 1)
Y = alambres[alambre]['mediciones'][y].reshape(-1, 1)
model.fit(X,Y)

Is there any chance to solve it by doing something like:

model.fit([X,X**2],Y)

Answer 1

Use PolynomialFeatures.

import numpy as np
from sklearn.preprocessing import PolynomialFeatures

x = np.array([[1,],[2,],[3,]])
X = PolynomialFeatures(degree=2).fit_transform(x)
X

Output:

array([[1., 1., 1.],
       [1., 2., 4.],
       [1., 3., 9.]])

Answer 2

You can use numpy's polyfit.

import numpy as np
from matplotlib import pyplot as plt
X = np.linspace(0, 100, 50)
Y = 23.24 + 2.2*X + 0.24*(X**2) + 10*np.random.randn(50) #added some noise
coefs = np.polyfit(X, Y, 2)
print(coefs)
p = np.poly1d(coefs)
plt.plot(X, Y, "bo", markersize= 2)
plt.plot(X, p(X), "r-") #p(X) evaluates the polynomial at X
plt.show()

Out:

[  0.24052058   2.1426103   25.59437789]