# Plotting Polynomial Regression?

I'm reading through Hands-On Machine Learning with Scikit-learn and Tensorflow by Geron. I am creating a simple polynomial regression using sklearn's PolynomialFeatures.

First, I create an X and y set using numpy random numbers with quadratic shape:

m = 100
X = 6 * np.random.rand(m, 1) - 3
y = 0.5 * X**2 + X + 2 + np.random.randn(m, 1)


Then I plot the scatterplot distribution:

plt.plot(X, y, "b.")
plt.xlabel("$$x_1$$", fontsize=18)
plt.ylabel("$$y$$", rotation=0, fontsize=18)
plt.axis([-3, 3, 0, 10])
plt.show()


Then I use PolynomialFeatures to add the 2nd degree:

poly_features = PolynomialFeatures(degree=2, include_bias=False)
X_poly = poly_features.fit_transform(X)


Then I fit the LinearRegression:

lin_reg = LinearRegression()
lin_reg.fit(X_poly, y)
lin_reg.intercept_, lin_reg.coef_


Then I plot the same distribution with the quadratic regression line. My question is with the following code:

X_new=np.linspace(-3, 3, 100).reshape(100, 1)
X_new_poly = poly_features.transform(X_new)
y_new = lin_reg.predict(X_new_poly)
plt.plot(X, y, "b.")
plt.plot(X_new, y_new, "r-", linewidth=2, label="Predictions")
plt.xlabel("$$x_1$$", fontsize=18)
plt.ylabel("$$y$$", rotation=0, fontsize=18)
plt.legend(loc="upper left", fontsize=14)
plt.axis([-3, 3, 0, 10])
plt.show()


Why do we create X_new (np.linspace(-3,3,100).reshape(100,1) and X_new_poly? Why does this not work with the X_poly that I've already created? (I tried plotting it with the original X_poly and it definitely does not work. It's just oscillating lines up and down over and over. I'm just not sure why this is the case.)

You could use X and lin_reg.predict(X_poly), but
1. The plot will put those points in the order they appear in X, and since you're using a line connector it will appear to jump all over the place. You could fix this by using a scatterplot instead.
2. It's vaguely disingenuous to use the training set's x-values for plotting the fitted curve; using np.linspace to get equally-spaced x-values is preferable (even if your original X was randomly generated and should fill the space reasonably well).