mean squared error

The loss function used in regression is called mean squared error

where:

Incorporating that loss function into the cost function :

Code

import numpy as np 
 
def compute_cost(X, y, w, b): 
"""
compute cost
Args:
X (ndarray (m,n)): Data, m examples with n features
y (ndarray (m,)) : target values
w (ndarray (n,)) : model parameters  
b (scalar)       : model parameter
 
Returns:
cost (scalar): cost
"""
m = X.shape[0]
cost = 0.0
for i in range(m):                                
f_wb_i = np.dot(X[i], w) + b           #(n,)(n,) = scalar (see np.dot)
cost = cost + (f_wb_i - y[i])**2       #scalar
cost = cost / (2 * m)                      #scalar    
return cost
 
cost = compute_cost(X_train, y_train, w_init, b_init)