import numpy as np
import matplotlib.pyplot as plt

def calculate_slope_intercept(x_values, y_values):
    """
    Calculate the slope and intercept of a regression line.
    @param x_values the independent x values.
    @param y_values the dependent y values.
    @return a list of the slope and y-intercept of the line.
    """
    x = np.array(x_values)
    y = np.array(y_values)
    
    n = len(x)
    sum_x = np.sum(x)
    sum_y = np.sum(y)
    sum_xx = np.sum(x*x)
    sum_xy = np.sum(x*y)
    
    numerator = sum_xy - (sum_x*sum_y)/n
    denominator = sum_xx - ((sum_x*sum_x)/n)
    
    m = numerator/denominator
    b = (np.mean(y) - m*np.mean(x))
    
    return m, b  # slope and intercept

def show_least_squares_line(title, x_label, y_label, 
                            x_values, y_values):
    """
    @param title the chart title.
    @param x_label the x-axis label.
    @param y_label the y-axis label.
    @param x_values the independent x values to plot.
    @param y_values the dependent y values to plot.
    """
    # First show the scatter plot.
    plt.scatter(x_values, y_values)
    
    # Now show the least squares line.
    m, b = calculate_slope_intercept(x_values, y_values)
    reg_line = [m*x + b for x in x_values]  # regression line
    plt.plot(x_values, reg_line, color='red')

    plt.title(f'{title}, m = {m:.2f}, b = {b:.2f}')
    plt.xlabel(x_label)
    plt.ylabel(y_label)

    plt.show()