bias 질문있습니다.

안녕하세요 강사님 PolynomialFeatures() 파라미터인 include_bias 를 True 로 설정하면 그래프 오차가 상당히 크게 나오는데 언제 왜 쓰이는지 궁금합니다.

import numpy as np

from matplotlib import pyplot as plt

from sklearn.preprocessing import PolynomialFeatures

from sklearn.linear_model import LinearRegression

m = 100

X = 6*np.random.rand(m, 1) - 3

y = 0.5 * X**2 + X +2+ np.random.randn(m, 1)

poly_features = PolynomialFeatures(degree=2, include_bias=False)

X_poly = poly_features.fit_transform(X)

#print(X_poly)

lin_reg = LinearRegression()

lin_reg.fit(X_poly, y)

print(lin_reg.intercept_, lin_reg.coef_)

poly_features2 = PolynomialFeatures(degree=2, include_bias=True)

X_poly2 = poly_features2.fit_transform(X)

lin_reg2 = LinearRegression()

lin_reg2.fit(X_poly2, y)

print(lin_reg2.intercept_, lin_reg2.coef_)

plt.plot(X, y, 'o')

plt.plot(X, lin_reg.coef_[0][1]* X**2 + lin_reg.coef_[0][0]*X +lin_reg.intercept_, 'r.')

plt.plot(X, lin_reg2.coef_[0][1]* X**2 + lin_reg2.coef_[0][0]*X +lin_reg2.intercept_, 'g.')

plt.plot(X, np.round(model.named_steps['linear'].coef_, 2)[0][1]* X**2 + np.round(model.named_steps['linear'].coef_, 2)[0][0]*X , 'y.')

plt.show()

from sklearn.pipeline import Pipeline

model = Pipeline([('Poly', PolynomialFeatures(degree=2, include_bias=False)),

                  ('linear', LinearRegression())])

model = model.fit(X, y)

print('회귀계수 : ', np.round(model.named_steps['linear'].coef_, 2))