QUESTION $3$

Consider a linear regressor. Each input has $n$ features as $x=[1,x_1,x_2,$dots,$x_d].$ The output is calculated

as:

$h(x)=w_0+w_1{x}_1+w_2{x}_2+$cdots$+w_d{x}_d$

$($a$)$ Given $n$ training examples as $(x^{(i)},y^{(i)})$ for $i=1,2,$dots,$n,$ write the mean square error loss

function $J(w)$ with $w=[1,w_1,w_2,$dots,$w_d]$

$($b$)$ Derive the gradient descent update rule for the weights $w_j,j=1,2,$dots,$d.$