def r_squared(x, y):
""" Return the coeffecient of determination (the squared correlation) of
the x, y pairs """
return (covariance(x,y))**2 / float(variance(x)*variance(y))
def least_squares_fit(x, y):
""" given training values for x,y computes the least squares values for
beta_0 and beta_1"""
beta_1 = covariance(x,y)/variance(x)
beta_0 = mean(y) - beta_1 * mean(x)
return beta_0, beta_1