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

style.use('fivethirtyeight')

xs = np.array([1,2,3,4,5,6], dtype = np.float64)
ys = np.array([5,4,6,5,6,7], dtype = np.float64)

def best_fit_slope_and_intercept(xs, ys):
	m = (  ((mean(xs)*mean(ys)) - mean(xs*ys)) / 
		((mean(xs)*mean(xs)) - mean(xs*xs)) )  

	b = ( mean(ys) -(m* mean(xs)) )
	return m, b

def squared_error(ys_orig, ys_line):
	return sum((ys_line - ys_orig)**2)

# r is co-efficient of determination
 
def coefficient_of_determination(ys_orig, ys_line):
	y_mean_line = [mean(ys_orig) for y in ys_orig]
	squared_error_regr = squared_error(ys_orig, ys_line)
	squared_error_y_mean = squared_error(ys_orig, y_mean_line)
	return 1 - (squared_error_regr/squared_error_y_mean)

m, b = best_fit_slope_and_intercept(xs, ys)

regression_line = [(m*x)+b for x in xs]

predict_x = 1.5
predict_y = (m*predict_x + b)


r_squared = coefficient_of_determination(ys, regression_line)
print(r_squared)

plt.scatter(xs, ys)
plt.scatter(predict_x, predict_y, color='g')
plt.plot(xs, regression_line)
plt.show()

