Manual Linear Regression

import matplotlib.pyplot as plt
import numpy as np
from matplotlib import style

style.use('dark_background')
X, Y = np.arange(1950, 2015, 5), [2558, 2782, 3043, 3350, 3712, 4089, 4451, 4855, 5287, 5700, 6090, 6474, 6864]
x = np.linspace(1950, 2015, 5)

X_Mean, Y_Mean = sum(X)/len(X), sum(Y)/len(Y)
Sxx, Sxy = sum([(x - X_Mean)**2 for x in X]), sum([(X[i]-X_Mean)*(Y[i]-Y_Mean) for i in range(len(X))])

B1 = Sxy / Sxx
B0 = Y_Mean - B1*X_Mean
y = B0 + B1*x
def G(x): return B0 + B1*x

for currentYear in X:
    plt.plot(currentYear, G(currentYear), 'ro', color="red")

plt.title(f'G(X) = {int(B0)} + {int(B1)}x')
plt.plot(x, y, color='red')
plt.plot(X, Y, 'ro', color='white')
plt.show()