The Loss After One Step Downhill

Gradient descent is used to fit a line $\hat{y} = b_0 + b_1 x$ to the four points

$(1,\,2), \quad (2,\,3), \quad (3,\,5), \quad (4,\,6)$

The loss is the mean squared error

$J(b_0, b_1) = \frac{1}{n}\sum_{i=1}^{n}\left(b_0 + b_1 x_i - y_i\right)^2$

and the parameters are updated with

$b_0 := b_0 - \eta \,\frac{2}{n} \sum (\hat{y}_i - y_i), \qquad b_1 := b_1 - \eta \,\frac{2}{n} \sum (\hat{y}_i - y_i)\,x_i$

Training starts at $b_0 = 0.5$ and $b_1 = 1.0$ with learning rate $\eta = 0.1$. Both parameters are updated simultaneously, each gradient computed from the predictions at the starting values.

Exactly one step is taken. What is the value of the loss $J$ at the new parameters?

Round your answer to 2 decimal places.