Greetings! I have a question about the codes in the function compute_cost . Specifically, why cost_sum is equal to 0 first, then cost_sum = cost + cost_sum later in the loop ?
Is there a mathematical reason for that, or is it for the loop’s sake? And which part of the lecture covers or relates to this code?
I look forward to hearing your answers.
Hi there 
So in that cell, if you look at the two cells above, you can see the math behind calculating the cost function.
J(w,b) = \frac{1}{2m} \sum\limits_{i = 0}^{m-1} (f_{w,b}(x^{(i)}) - y^{(i)})^2 \tag{1}
As you can see, the total cost is a sum. Now all that the loop does is calculate that sum.
# number of training examples
m = x.shape[0] # take the number of examples in the training data.
cost_sum = 0 # initialize the sum to zero (to store the result of the sum)
for i in range(m):
f_wb = w * x[i] + b # this is the prediction of our model for each x, given w and b
cost = (f_wb - y[i]) ** 2 # this is the squared error for that sample. (remember that our cost is the Mean Squared Error i.e. MSE)
cost_sum = cost_sum + cost # add the cost of this sample, to the sum
total_cost = (1 / (2 * m)) * cost_sum # now we have the sum. we devide by (2 * m) as shown in the equation.
return total_cost
Here I tried to comment the code to be more readable. Tell me if your question remains.
The goal is to compute the total cost by adding together the portion of the cost that is calculated for each example. That’s what “cost_sum = cost_sum + cost” does.
First the total cost has to be set to 0, so that this line of code has something to reference on the fist pass through the for-loop.