Q$\mathrm{.}1.$ Consider the following streaming version of linear regression algorithm.

Algorithm StreamingSimpleLinearRegresssionModel

Double sumX $=0\mathrm{.}0,$ sumY $=0\mathrm{.}0,$ sumXY $=0\mathrm{.}0,$ sumX$2=0\mathrm{.}0,$ a $=0\mathrm{.}0,$ b $=0\mathrm{.}0$

Double n

Boolean dirty $=$ true

Update$()$

If $(!$dirty$)$ then return

b $=($ sumXY $($sumX $*$ sumY$)/$ n $)/($ sumX$2($sumX $*$ sumX$)/$ n $)$

a $=($sumY $/$ n$)($b $*$ sumX $/$ n$)$

dirty $=$false

observe $($double y$,$ double x$)$

sumX $+=$ x

sumY $+=$ y

sumXY $+=$ x $*$ y

sumX$2+=$ x $*$ x

n $+=1$

dirty $=$ true

double getB$()$

update$()$

return b

double getA$()$

update$()$

return a

Following $5$ pairs of stream data values are passed through the above model.

X $33554$

Y $589107$

$($A$)$What will be the coefficients $$a$$ and $$b$$ after model has processed second tuple? $[2]$

$($B$)$What will be the model expression when the model has processed first four tuples? $[4]$

$($C$)$After processing all the five tuples, what will be the prediction done by model for x $=1?[2]$