polynomial degree scatter graph points not fitting for linear regression

Question

I am using sklearn linear and polynomial feature to fit to a data set. the code looks like below. I am plotting the points using scatter but they don't seem to align with the prediction values. not sure what i am missing. i have tried to change degree value from 1 to 20 but no effect.

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

DEGREE = 5

X = np.array([276237,276617, 276997,  277377, 277757, 278137, 278517, 278897,  279277, 279657]).reshape(-1, 1)
y = np.array([6, 8, 2, 4, 0, 1, 7, 0, 1, 4])

poly_feat = PolynomialFeatures(degree=DEGREE)
X_poly = poly_feat.fit_transform(X)

lm = LinearRegression(fit_intercept = False)
lm.fit(X_poly, y)

fig=plt.figure()
ax=fig.add_axes([0,0,1,1])
ax.scatter(X, lm.predict(X_poly), color='r')
ax.set_xlabel('Total Amount')
ax.set_ylabel('Days to mine')
ax.plot(X,y)
plt.show()

Answer 1

I guess it is because you do not have enough data. You have 5 degree polynomial but only 10 data. The model doesn't train well. I tried made up some data and found that your code works well:

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

BLOCK_REWARD = 380
DEGREE = 5

#X = np.array([276237,276617, 276997,  277377, 277757, 278137, 278517, 278897,  279277, 279657]).reshape(-1, 1)
#y = np.array([6, 8, 2, 4, 0, 1, 7, 0, 1, 4])

# New data
n = 50
X = np.linspace(-5, 5, n)
y = X**5 - 3 * X**4 + 2 * X**3 + 4 * X**2 - X + 6 + 200*np.random.randn(n)
X = X.reshape(-1, 1)

# Everything remain unchange
poly_feat = PolynomialFeatures(degree=DEGREE)
X_poly = poly_feat.fit_transform(X)

lm = LinearRegression(fit_intercept = False)
lm.fit(X_poly, y)

fig=plt.figure()
ax=fig.add_axes([0,0,1,1])
ax.scatter(X, lm.predict(X_poly), color='r')
ax.set_xlabel('Total Amount')
ax.set_ylabel('Days to mine')
ax.plot(X,y)
plt.show()