$(25$ points$)$ Consider the regression$-$based cost function

$f(w_1,w_2,w_3)=\frac{1}{50}{\displaystyle \underset{i=1}{\overset{50}{}}}\frac{1}{2}(y(w,x_i)-t_i{)}^2$

where the $x$ and $t$ values are given in the file, and the model function is given by

$y(w,x)=w_1+(x-w_2{)}^2+$exp$(-w_{3}x)$

In this problem you will evaluate taking one step of gradient descent using different methods. In each

case, initialize your guess for the $w$ parameters with the zero vector, and use a step size of $=0\mathrm{.}5.$

$($a$)$ Compute one step of gradient descent $($i$.$e$.,$ using the entire dataset$).$ Give the $w$ vector after the

step and compute the cost function values before and after the step.