$($h$)[$AIR$6002]$ The closed form solution for linear regression with least squares is

$w=({\displaystyle \underset{i=1}{\overset{N}{}}}{x}_i{x}_i^T{)}^{-1}({\displaystyle \underset{i=1}{\overset{N}{}}}{x}_i{y}_i).$

Compute this analytical solution. Does the result match up with what you got from SGD$?$

$[3$ points$]$

Answer the remaining questions in $1-2$ short sentences.

$($i$)[$AIR$6002]$ Is there any reason to use SGD when a closed form solution exists?

$[3$ points$]$

$($j$)[$AIR$6002]$ Based on the SGD convergence plots that you generated earlier, describe a stop$-$

ping condition that is more sophisticated than a pre$-$defined number of epochs.

$[3$ points$]$

$($k$)[$AIR$6002]$ How does the convergence behavior of the weight vector differ between the per$-$

ceptron and SGD algorithms?