Assume that we are training a multivariate linear regression model using three instances as follows.

instance id: $,(x_1,x_2),$ label $y$

instance $1$:

instance $2$: $(-0\mathrm{.}5,1),1$

instance $3$: $(2,0\mathrm{.}5),1$

The cost function is based on mean squared error as follows.

$mi{n}_{{}_0,{}_1,{}_2}\frac{1}{6}{\displaystyle \underset{i=1}{\overset{3}{}}}(h_{}(x^{(i)})-y^{(i)}{)}^2.$

Assume that we have initialized

$w=[{}_0,{}_1,{}_2]=[0,0\mathrm{.}5,1].$

You apply gradient descent algorithm to compute a $w$ that minimizes the cost function w$.$r$.$t$.$ the three

given instances. Assume that in the first iteration, we set learning rate $=0\mathrm{.}8.$ In the second iteration,

we set learning rate $=0\mathrm{.}4.$ Please concisely show how $w$ is updated in the first and second iterations.