Python/ML Exercise Computes Cost Function Linear Regresion

py-ml-cost-fn-linear-regression.py

import numpy as np
import matplotlib.pyplot as plt

def compute_cost(x, y, w, b):
  """
  Computes the cost function for linear regression.

  Args:
      x (ndarray): Shape (m,) Input to the model (Population of cities)
      y (ndarray): Shape (m,) Label (Actual profits for the cities)
      w, b (scalar): Parameters of the model

  Returns
      total_cost (float): The cost of using w,b as the parameters for linear regression
             to fit the data points in x and y
  """
  # number of training examples
  m = x.shape[0]
  
  ### START CODE HERE ###
  cost_sum = 0
  
  for i in range(m):
    f_wb = w * x[i] + b
    
    cost = (f_wb - y[i]) ** 2
    
    cost_sum = cost_sum + cost
  
  ### END CODE HERE ###
  
  total_cost = (1 / (2 * m)) * cost_sum
  
  return total_cost

x_data = np.array([ 6.1101,  5.5277,  8.5186,  7.0032,  5.8598,  8.3829,  7.4764,
        8.5781,  6.4862,  5.0546,  5.7107, 14.164 ,  5.734 ,  8.4084,
        5.6407,  5.3794,  6.3654,  5.1301,  6.4296,  7.0708,  6.1891,
       20.27  ,  5.4901,  6.3261,  5.5649, 18.945 , 12.828 , 10.957 ,
       13.176 , 22.203 ,  5.2524,  6.5894,  9.2482,  5.8918,  8.2111,
        7.9334,  8.0959,  5.6063, 12.836 ,  6.3534,  5.4069,  6.8825,
       11.708 ,  5.7737,  7.8247,  7.0931,  5.0702,  5.8014, 11.7   ,
        5.5416,  7.5402,  5.3077,  7.4239,  7.6031,  6.3328,  6.3589,
        6.2742,  5.6397,  9.3102,  9.4536,  8.8254,  5.1793, 21.279 ,
       14.908 , 18.959 ,  7.2182,  8.2951, 10.236 ,  5.4994, 20.341 ,
       10.136 ,  7.3345,  6.0062,  7.2259,  5.0269,  6.5479,  7.5386,
        5.0365, 10.274 ,  5.1077,  5.7292,  5.1884,  6.3557,  9.7687,
        6.5159,  8.5172,  9.1802,  6.002 ,  5.5204,  5.0594,  5.7077,
        7.6366,  5.8707,  5.3054,  8.2934, 13.394 ,  5.4369])

y_data = np.array([17.592  ,  9.1302 , 13.662  , 11.854  ,  6.8233 , 11.886  ,
        4.3483 , 12.     ,  6.5987 ,  3.8166 ,  3.2522 , 15.505  ,
        3.1551 ,  7.2258 ,  0.71618,  3.5129 ,  5.3048 ,  0.56077,
        3.6518 ,  5.3893 ,  3.1386 , 21.767  ,  4.263  ,  5.1875 ,
        3.0825 , 22.638  , 13.501  ,  7.0467 , 14.692  , 24.147  ,
       -1.22   ,  5.9966 , 12.134  ,  1.8495 ,  6.5426 ,  4.5623 ,
        4.1164 ,  3.3928 , 10.117  ,  5.4974 ,  0.55657,  3.9115 ,
        5.3854 ,  2.4406 ,  6.7318 ,  1.0463 ,  5.1337 ,  1.844  ,
        8.0043 ,  1.0179 ,  6.7504 ,  1.8396 ,  4.2885 ,  4.9981 ,
        1.4233 , -1.4211 ,  2.4756 ,  4.6042 ,  3.9624 ,  5.4141 ,
        5.1694 , -0.74279, 17.929  , 12.054  , 17.054  ,  4.8852 ,
        5.7442 ,  7.7754 ,  1.0173 , 20.992  ,  6.6799 ,  4.0259 ,
        1.2784 ,  3.3411 , -2.6807 ,  0.29678,  3.8845 ,  5.7014 ,
        6.7526 ,  2.0576 ,  0.47953,  0.20421,  0.67861,  7.5435 ,
        5.3436 ,  4.2415 ,  6.7981 ,  0.92695,  0.152  ,  2.8214 ,
        1.8451 ,  4.2959 ,  7.2029 ,  1.9869 ,  0.14454,  9.0551 ,
        0.61705])

EXPECTED_COST = 75.203
cost = round(compute_cost(x_data, y_data, 2, 1),3)
assert cost == EXPECTED_COST
print(type(cost))
print(f'Cost at initial w: {cost:.3f}')

# -----
plt.scatter(x_data, y_data, marker='x', c='r')
plt.title("Profits vs. Population per city")
plt.ylabel('Profit in $10,000')
plt.xlabel('Population of City in 10,000s')
plt.show()