$(20$Pts$)$ Advanced "Linear Regression"

Assume the model is $y={}_0\frac{1}{x}.$

And the loss function is Loss$(y,$hat$(y))={\displaystyle \underset{?}{\overset{?}{}}}(y-$hat$(y){)}^2.$

You have $2$ data points which are $(1,2)$ and $(2,1).$ Currently the ${}_0=1.$

Is ${}_0=1$ the correct parameter for the model based on the given data?

If not, please calculate the derivative with respect to ${}_0$ and update the ${}_0$ using

the gradient descent for one step. Here, let's set the learning rate $=0\mathrm{.}2.$