linear_regression.py

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

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 create_dataset(hm, variance, step=2, correlation=False):
    val = 1
    ys = []
    for i in range(hm):
        y = val + random.randrange(-variance, variance)
        ys.append(y)
        if correlation and correlation == 'pos':
            val += step
        elif correlation and correlation == 'neg':
            val -= step
    xs = [i for i in range(len(ys))]
    return np.array(xs, dtype=np.float64), np.array(ys, dtype=np.float64)



def best_fit_slope_and_intercept(xs, ys):
    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):
    return sum((ys_orig  - ys_line)**2)

def coefficient_of_determination(ys_orig, ys_line):
    y_mean_line = [mean(ys_orig) for _ 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)


xs, ys = create_dataset(40, 2 , 2, correlation='pos')

m, b = best_fit_slope_and_intercept(xs, ys)


regresion_line = [m * x + b for x in xs]
predict_x = 8
predict_y = m * predict_x + b

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

plt.scatter(xs, ys)
plt.scatter(predict_x, predict_y, color='green')
plt.plot(xs, regresion_line)
plt.show()

print(m, b)