Cost Function

We can measure the accuracy of our hypothesis function by using acost function. This takes an average difference (actually a fancier version of an average) of all the results of the hypothesis with inputs from x's and the actual output y's.

J(θ0,θ1)=12m∑i=1m(y^i−yi)2=12m∑i=1m(hθ(xi)−yi)2

To break it apart, it is12x¯wherex¯is the mean of the squares ofhθ(xi)−yi, or the difference between the predicted value and the actual value.

This function is otherwise called the "Squared error function", or "Mean squared error". The mean is halved(12)as a convenience for the computation of the gradient descent, as the derivative term of the square function will cancel out the12term. The following image summarizes what the cost function does: