$15\mathrm{.}15$ Given the data

$\backslash$table$[[x,5,10,15,20,25,30,35,40,45,50],[y,17,24,31,33,37,37,40,40,42,41]]$

use least$-$squares regression to fit $($a$)$ a straight line, $($b$)$ a power equation, $($c$)$ a saturation$-$growth$-$rate equation, and $($d$)$ a parabola. For $($b$)$ and $($c$),$ employ transformations to linearize the data. Plot the data along with all the curves. Is any one of the curves superior? If so$,$ justify.