Question $3$: Write a program to fit a curve to the following sets of data:

$x=[1,2,3,5,15,25,40,60]$

Set$1=[0\mathrm{.}5,0\mathrm{.}3,0\mathrm{.}8,1,1\mathrm{.}5,0\mathrm{.}5,1,2]$

Set $2=[45,46,44\mathrm{.}5,45,44\mathrm{.}8,45\mathrm{.}5,45,48]$

Fit Set$1$ vs $x$ and Set$2$ vs $x.$ Ask the user to select the type of fitting from the following options: Polynomial and Exponential and select the order of $1$ and $2$ for both fitting types.

Try all the fittings and asses the goodness of fit in terms of r$-$squared values.

Provide all the plots for all $4$ options with their corresponding least$-$square criterion, sum of the squares of deviation, and r$-$squared values. Make sure the data and the fittings for each option are all included on their corresponding plot. Ensure the plots are properly prepared based on the notes at the beginning of this document.

Do you think the scaling will improve the fitting? If the answer is yes, please find the improved $r$ squared for each option.