Andrew Ng’s machine learning week2 experiment answers Practice Lab Linear Regression [C1_W2_Linear_Regression]

Practice Lab: Linear Regression

Exercise 1

Complete the compute_cost below to:

• Iterate over the training examples, and for each example, compute:

  • The prediction of the model for that example
    $$f_{wb}(x^{(i)})=w{x}^{(i)}+b$$

  • The cost for that example $$cos{t}^{\left(i\right)}=(f_{wb}-y^{\left(i\right)}{)}^2$$

• Return the total cost over all examples
  $$J(\mathbf{w},b)=\frac{1}{2m\_}\sum _{i=0}^{m-1}cos{t}^{(i)}$$

  • Here, $m$ is the number of training examples and $\sum$ is the summation operator

If you get stuck, you can check out the hints presented after the cell below to help you with the implementation.

# UNQ_C1
# GRADED FUNCTION: compute_cost

def compute_cost(x, y, w, b): 
    # number of training examples
    m = x.shape[0] 
    # You need to return this variable correctly
    total_cost = 0
    
    ### START CODE HERE ###  
    for i in range(m):
        total_cost+=((x[i]*w+b)-y[i])**2
    total_cost=total_cost/(2*m)
    ### END CODE HERE ### 
    
    return total_cost

Exercise 2

Please complete the compute_gradient function to:

• Iterate over the training examples, and for each example, compute:

  • The prediction of the model for that example
    $$f_{wb}(x^{(i)})=w{x}^{(i)}+b$$

  • The gradient for the parameters $w,b$ from that example
    $${\frac{\partial J(w,b)}{\partial b}}^{\left(i\right)}=(f_{w,b}(x^{\left(i\right)})-y^{(i)})$$
    $${\frac{\partial J(w,b)}{\partial w}}^{(i)}=(f_{w,b}(x^{(i)})-y^{(i)})x^{\left(i\right)}$$

• Return the total gradient update from all the examples
  $$\frac{\partial J(w,b)}{\partial b}=\frac{1}{m}\sum _{i=0}^{m-1}{\frac{\partial J(w,b)}{\partial b}}^{(i)}$$

  $$\frac{\partial J(w,b)}{\partial w}=\frac{1}{m}\sum _{i=0}^{m-1}{\frac{\partial J(w,b)}{\partial w}}^{\left(i\right)}$$

  • Here, $m$ is the number of training examples and $\sum$ is the summation operator

If you get stuck, you can check out the hints presented after the cell below to help you with the implementation.

# UNQ_C2
# GRADED FUNCTION: compute_gradient
def compute_gradient(x, y, w, b):   
    # Number of training examples
    m = x.shape[0]
    # You need to return the following variables correctly
    dj_dw = 0
    dj_db = 0
    
    ### START CODE HERE ### 
    for i in range(m):
        f_wb=w*x[i]+b
        dj_dw_i=(f_wb-y[i])*x[i]
        dj_db_i=f_wb-y[i]
        dj_dw+=dj_dw_i
        dj_db+=dj_db_i
    dj_dw=dj_dw/m
    dj_db=dj_db/m
    ### END CODE HERE ### 
        
    return dj_dw, dj_db