Coef and Polynomial equation I have a problem about the coef of polynomial, from machine learning.
clf = linear_model.LinearRegression()
train_y_ = clf.fit(train_x_poly, train_y)
# The coefficients
print ('Coefficients: ', clf.coef_)
print ('Intercept: ',clf.intercept_)

Coefficients:  [[ 0.         50.98399588 -1.59089505]]
Intercept:  [106.67723923]
plt.scatter(train.ENGINESIZE, train.CO2EMISSIONS,  color='blue')
XX = np.arange(0.0, 10.0, 0.1)
yy = clf.intercept_[0]+ clf.coef_[0][1]*XX+ clf.coef_[0][2]*np.power(XX, 2)
plt.plot(XX, yy, '-r' )
plt.xlabel("Engine size")
plt.ylabel("Emission")


My question is about this equation:
yy = clf.intercept_[0]+ clf.coef_[0][1]*XX+ clf.coef_[0][2]*np.power(XX, 2)

why they do not use the first coef [0][0], is because is '0'?

Most probably, they don't use it because the coefficient is $0$. It is $0$ because the first coefficient of a polynomial feature generator in sklearn library is constant. Here is their explanation:

For example, if an input sample is two dimensional and of the form [a,
b], the degree-2 polynomial features are $[1, a, b, a^2, ab, b^2]$.

When the first feature is constant and you also fit the intercept in LinearRegression (LR), one of them becomes redundant. And, the constant feature is redundant because the fit procedure first standardizes the features, make them zero mean and unit variance (if possible). The constant feature, which is full $1$'s becomes a full $0$'s vector and whatever coefficient you multiply will have no effect. This is why it makes sense to have that coefficient $0$.
