c$)$ Given the inomalired dataset below and $w=1\mathrm{.}5$ and $b=0\mathrm{.}5,$ our objective is to develop

a model that can predict bouse price based on house size

$y_{\text{p}\text{r}\text{e}\text{d}}=wx+b$

$L=\frac{1}{2}(y_{\text{p}\text{r}\text{e}\text{d}}-y{)}^2$

$w_{\text{n}\text{e}\text{x}\text{c}}=w_{\text{d}\text{i}\text{d}}-\frac{\text{d}\text{e}\text{l}\text{L}}{\text{d}\text{e}\text{l}\text{w}}$

$\frac{\text{d}\text{e}\text{l}\text{L}}{\text{d}\text{e}\text{l}\text{w}}=(y_{\text{p}\text{e}\text{d}}-y)x$

$\frac{\text{d}\text{e}\text{l}\text{L}}{\text{d}\text{e}\text{l}\text{b}}=(y_{\text{p}\text{e}\text{d}}-y)$

$b_{\text{R}\text{e}\text{w}}=b_{\text{d}\text{i}\text{d}}-\frac{\text{d}\text{e}\text{l}\text{L}}{\text{d}\text{e}\text{l}\text{b}}$

i$.$ Using a lcarning rate $(a)$ of $0\mathrm{.}5$ and the MSE loss function $($L$)$ as your loss function,

after one step of the siochastic gradient descent, answer the questions below. $($Show

all working., Note you can we any row as the sample.

Calculate the lose.

$[1$ mark$]$

Calculate new valoes for $w$ and $b.$

$[3$ marks$]$

ii$.$ How many parameter updates woold be done for the dataset above in the

following scenarios

Stochastic gradient deseens and $300$ epochs.

$[1$ mark$]$

Mini batch stochastic gradient deseent batch sixe of $3$ and $400$ epocts.

$[1$ mark$]$