Regression problem: using $4$ data points in Table $1($below$),$ we will find the best fit.

$\backslash$table$[[$X$,1,3,4,5],[$Y$,2,160,510,1250]]$

Table $1$: For problem $3$

a$)(3$ points$)$ Find the best linear fit so that $Y=ax+b$ has minimal least squares. To receive credit you must show yourself applying the analytic expressions for a and $b$ from class.

b$)(0$ points$)$ Clearly that's a bad fit $($plot it to see for yourself, but not needed for the assignment$).$ Make a guess as to what power of $x$ fits the curve following a $Y=a{x}^{b}ft?$

c$)(4$ points$)$ Apply the power$-$law version of linear regression to find the best fit estimate for a and $b.$ Note that the values will not be perfectly clean, but you must show yourself applying the appropriate formulae and solving for the values.