main.py

import numpy as np

x_values = np.array([1,2,3,4,5,6,7,8,9,10])
y_values = np.array([1,4,1,6,4,7,4,6,10,8])

def best_fit_line(x_values,y_values):
    m = (((x_values.mean() * y_values.mean()) - (x_values * y_values).mean() ) /
         ( (x_values.mean()) ** 2 - (x_values ** 2 ).mean() ))

    b = y_values.mean() - m * x_values.mean()

    return m, b

m, b = best_fit_line(x_values, y_values)

print(f"regression line: y = {round(m,2)}x + {round(b,2)}")

x_prediction = 15
y_prediction = (m * x_prediction)+b
print(f"predicted coordinate: ({round(x_prediction,2)}, {round(y_prediction,2)})")

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

def squared_error(ys_orig, ys_line):
    return sum((ys_line - ys_orig) * (ys_line - ys_orig)) # helper function to return the sum of the distances between the two y values squared

def r_squared_value(ys_orig,ys_line):
    squared_error_regr = squared_error(ys_orig, ys_line) # squared error of regression line
    y_mean_line = [ys_orig.mean() for y in ys_orig] # horizontal line (mean of y values)
    squared_error_y_mean = squared_error(ys_orig, y_mean_line) # squared error of the y mean line
    return 1 - (squared_error_regr/squared_error_y_mean)

r_squared = r_squared_value(y_values, regression_line)
print(f"r^2 value: {round(r_squared,2)}")

import matplotlib.pyplot as plt

plt.title('Linear Regression')
plt.scatter(x_values, y_values,color='#5b9dff',label='data')
plt.scatter(x_prediction, y_prediction, color='#fc003f', label="predicted")
plt.plot(x_values, regression_line, color='000000', label='regression line')
plt.legend(loc=4)
plt.savefig("graph.png")