Linear Regression Cost Function

For one variable, the cost function for linear regression $J(w,b)$ is defined as

$J(w,b)=\frac{1}{2m}\sum _{i=0}^{m-1}(f_{w,b}(x^{(i)})-y^{(i)}{)}^2$

• You can think of $f_{w,b}(x^{(i)})$ as the model’s prediction of your Xbusiness profit, as opposed to $y^{(i)}$, which is the actual profit that is recorded in the data.
• $m$ is the number of training examples in the dataset

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] 
    
    # You need to return this variable correctly
    total_cost = 0
    
    ### START CODE HERE ###
    predicted_cost = w * x + b
    total_cost = (1/(2*m))*np.sum((predicted_cost - y)**2)
    ### END CODE HERE ### 
 
    return total_cost