def test_sum_of_squares_with_alternate_formula(x, y):
x = np.array(x, np.float64)
y = np.array(y, np.float64)
expected_value = 0
for index in range(0, len(y)):
expected_value += (y[index] - x[index]) ** 2
calculated_value = goodness_of_fit.residual_sum_of_squares(x, y)
assert_values_are_within_epsilon_distance(calculated_value, expected_value)
def test_r2_with_alternate_formula(observed, predicted):
"""
Is the R^2 calculation for x and predicted equals to a known quantity that is correct?
"""
observed = np.array(observed, np.float64)
predicted = np.array(predicted, np.float64)
m = np.mean(observed, dtype=np.float64)
total_sum_of_squares = np.sum(np.power(observed - m, 2))
residual_sum_of_squares = np.sum(np.power(observed - predicted, 2))
expected_value = 1 - (residual_sum_of_squares / total_sum_of_squares)
calculated_value = goodness_of_fit.coefficient_of_determination(observed, predicted)
assert_values_are_within_epsilon_distance(calculated_value, expected_value)
