$[20$ points$]$ Consider the following dataset:

$($a$)$ Fit the following model $($both by R and by hand$)$:

$Y={}_0+{}_{1}x+$

$($b$)$ Fit the following model $($both by R and by hand$)$:

$Y={}_{1}x+$

$($c$)$ Comment on the work you have done.