# 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:

![](https://1423730981-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-M5-0RGuSGVoyMc2kCFR%2F-M5-0RgMLg-NeST4zMsc%2F-M5-0U6bc4M50NCGyiY6%2FLinearRegression_CostFn.PNG?generation=1586990807665570\&alt=media)
