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)

# plt.scatter(xs, ys)
# plt.show()

def best_fit_slope_and_intercept(xs, ys):
    # least square method
    m = ((mean(xs) * mean(ys)) - mean(xs*ys)) / (mean(xs)**2 - mean(xs**2))
    b = mean(ys) - m*mean(xs)
    return m, b

def squared_error(ys_orig, ys_line):
    # calculate squared error
    return sum((ys_line-ys_orig)**2)

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)

# print (m, b)
regression_line = [(m*x)+b for x in xs]
# The line above is equal
# for x in xs:
#     regression_line.append((m*x)+b)

predict_x = 8
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()
