The formula of loss function uses '(i)' as power of expected and real variables. What does that mean?

Question

In the formula below, could one understand $y^{(i)}$ as $y_i$ ? If not, what is the fundamental difference ?

$$ j(\theta_0, \theta_1) = \frac{1}{2m}\sum_{i=1}^m(h_{\theta}(x^{(i)})-y^{(i)})^2 $$

Answer 1

You are correct, the $i$ superscript simply denotes an index of a single observation/sample in the dataset. $y^{(i)}$ then refers to the output/label of a single sample and $h_\theta(x^{(i)})$ is the model's prediction for a specific input.