Cost Function

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

If m is the number of training examples, the cost function for Linear Regression in One Variable is given by:

$J(θ_0,θ_1) = (1/2m) ∑_{i=1}^{m}(h_θ(x^{(i)})−y^{(i)})^2$

Lower values indicate more accuracy.

This function is otherwise called the "Squared error function", or Mean squared error.

We can plot it on a graph taking $θ_0$ and $θ_1$ on the x and z axis respectively, and J on the y axis: