I am not getting polynomial regression in sklearn smoothly

Question

For this code of polynomial regression implemented in python with sklearn

import numpy as np
import matplotlib.pyplot as plt
from sklearn.linear_model import LinearRegression
from sklearn.preprocessing import PolynomialFeatures
import pandas as pd

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

poly_features=PolynomialFeatures(3)
X_poly=poly_features.fit_transform(X)
lin_reg=LinearRegression()

X_new=[[0],[3]]

lin_reg.fit(X_poly,y)

plt.plot(X,y,"b.")
plt.plot(X, lin_reg.predict(poly_features.fit_transform(X)),  "r-")

plt.show()

The output is showing as

But I wanted to get a smooth prediction line. How to get it?

Answer 1

The problem is that X array is not sorted. So when you use lines -r to plot your data, it connects the data points in the order of your unsorted X-data points. Hence, you see a random network of lines. The order doesn't matter for the plot with markers because you are just plotting dots without lines.

The solution is to sort the X data and pass the sorted X data to your plot command and accordingly to the fit_transform.

shape = X.shape
X = np.sort(X.flatten())
plt.plot(X, lin_reg.predict(poly_features.fit_transform(X.reshape((shape)))),  "r-", lw=2)