Polynomial Regression

Polynomial Regression
Author

Benedict Thekkel 

import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import PolynomialFeatures
X = np.random.rand(100,1)
y = 4 + 5 * X + 1 * np.random.randn(100, 1)
plt.scatter(X, y)
plt.show()

reg = LinearRegression()
reg.fit(X, y)
LinearRegression()
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X_vals = np.linspace(0, 1, 100).reshape(-1,1)
y_vals = reg.predict(X_vals)
plt.scatter(X, y)
plt.plot(X_vals, y_vals, color ='g')
plt.show()

Second Order

X = 4 * np.random.rand(50,1) -2
y = 4 + 2 * X + 5 * X ** 2 + 2 * np.random.randn(50, 1)
poly_features = PolynomialFeatures(degree = 2, include_bias = False)
X_poly = poly_features.fit_transform(X)
reg1 = LinearRegression()
reg1.fit(X_poly, y)
LinearRegression()
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X_vals = np.linspace(-2, 2, 50).reshape(-1,1)
X_vals_poly = poly_features.transform(X_vals)
y_vals = reg1.predict(X_vals_poly)
plt.scatter(X, y)
plt.plot(X_vals, y_vals, color ='g')
plt.show()

X_vals_poly[:,1]
array([4.00000000e+00, 3.68013328e+00, 3.37359434e+00, 3.08038317e+00,
       2.80049979e+00, 2.53394419e+00, 2.28071637e+00, 2.04081633e+00,
       1.81424406e+00, 1.60099958e+00, 1.40108288e+00, 1.21449396e+00,
       1.04123282e+00, 8.81299459e-01, 7.34693878e-01, 6.01416077e-01,
       4.81466056e-01, 3.74843815e-01, 2.81549354e-01, 2.01582674e-01,
       1.34943773e-01, 8.16326531e-02, 4.16493128e-02, 1.49937526e-02,
       1.66597251e-03, 1.66597251e-03, 1.49937526e-02, 4.16493128e-02,
       8.16326531e-02, 1.34943773e-01, 2.01582674e-01, 2.81549354e-01,
       3.74843815e-01, 4.81466056e-01, 6.01416077e-01, 7.34693878e-01,
       8.81299459e-01, 1.04123282e+00, 1.21449396e+00, 1.40108288e+00,
       1.60099958e+00, 1.81424406e+00, 2.04081633e+00, 2.28071637e+00,
       2.53394419e+00, 2.80049979e+00, 3.08038317e+00, 3.37359434e+00,
       3.68013328e+00, 4.00000000e+00])
plt.scatter(X_vals, X_vals_poly[:,1])

Higher Order

X = 4 * np.random.rand(50,1) -2
y = 4 + 2 * X + 5 * X ** 2 + 12 * X ** 3 + 2 * X ** 4 + + 2 * np.random.randn(50, 1)

poly_features = PolynomialFeatures(degree = 4, include_bias = False)
X_poly = poly_features.fit_transform(X)

reg2 = LinearRegression()
reg2.fit(X_poly, y)

X_vals = np.linspace(-2, 2, 50).reshape(-1,1)
X_vals_poly = poly_features.transform(X_vals)
y_vals = reg2.predict(X_vals_poly)
plt.scatter(X, y)
plt.plot(X_vals, y_vals, color ='g')
plt.show()

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