Question #$7.$ Consider the following data set:

$x=\left[\begin{array}{ccccccc}1& 3& 5& 8& 10& 13& 17\end{array}\right]$;

$Y=\left[\begin{array}{cccccc}5& 2& 0& 6& 10& 15\end{array}\right]$;

a$)$ Create a third order best fit line for the provided data. Use the provided formulas to calculate the required coefficients.

b$)$ Solve for the third order coefficients using polyfit and compare your results to the ones from part a$.$

c$)$ Calculate the $r^2$ value for the created best fit equation.